Graph Neural Network (GNN)

The core computational mechanism where nodes iteratively aggregate feature information from their neighbors to update their own hidden states. In a distribution feeder, a transformer node receives voltage and current embeddings from adjacent line segments and loads. This process, formalized as neighborhood aggregation, allows the model to capture both local electrical properties and wider topological context without requiring a fixed input size. After k layers of message passing, a node's representation encodes information from its k-hop neighborhood, effectively capturing the receptive field of protection zones.

GNNs produce identical outputs regardless of the arbitrary ordering of nodes in the input adjacency matrix. This property is critical for power systems because bus numbering in network models is an administrative convention with no physical meaning. A GNN trained on one feeder topology will correctly process the same feeder regardless of how nodes are indexed, ensuring the model learns the actual electrical relationships rather than spurious positional correlations. This contrasts with convolutional neural networks, which assume a fixed grid structure.

Unlike transductive methods that require retraining when the graph structure changes, GNNs learn a function that generalizes to unseen nodes and entirely new graphs. For grid operators, this means a model trained on historical data from one substation can be deployed to a different feeder with a distinct topology without modification. This zero-shot transfer is essential for utilities managing thousands of heterogeneous circuits, as it eliminates the prohibitive cost of training bespoke models for each feeder configuration.

GNNs natively incorporate attributes on connections, not just nodes. In power systems, edges represent transmission lines with critical physical properties:

• Impedance (R + jX)
• Thermal rating (MVA limit)
• Line length and charging capacitance
• Switch status (open/closed) These edge features are embedded alongside node features during message passing, allowing the model to distinguish between a heavily loaded 12.47 kV line and a lightly loaded 69 kV line when predicting congestion patterns.

Two dominant paradigms exist for defining convolution on graphs:

Spectral methods operate in the Fourier domain using the graph Laplacian eigenvectors, providing a mathematically principled filter but struggling with variable topologies.

Spatial methods define convolution directly in the node domain by aggregating neighbor features, offering better scalability and inductive capability. For dynamic grid reconfiguration where switch states alter the Laplacian spectrum, spatial methods like GraphSAGE and GAT are preferred due to their robustness to topological changes.

Modern GNN architectures like Relational GCN and Heterogeneous Graph Transformer handle multiple node and edge types within a single graph. An electrical distribution network naturally maps to a heterogeneous schema:

• Node types: Buses, generators, transformers, loads, capacitor banks
• Edge types: Transmission lines, transformer windings, switches Each type maintains its own learnable projection matrix, allowing the model to process the distinct physics governing each asset class while sharing information across the unified topology.