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A Comparative Study of Graph Representations for GNN-Based Power Grid Control in L2RPN
Adrian Degenkolb, Qiong Huang, Benjamin Schäfer
TL;DR
Topology control in L2RPN requires graph representations, but prior studies rarely isolate graph construction from other RL design choices. This paper compares physical, electrical-sensitivity, and hybrid representations under a controlled GNN-PPO setup, finding that compact physical representations can outperform richer alternatives and that graph complexity should match task granularity.
Problem
Graph construction is an underexamined design choice in RL-based power-grid control, where GNN node and edge mappings determine state granularity, message-passing paths, and computational cost.
Method
The study compares ten graph representations and a non-graph MLP under fixed action space, training budget, evaluation set, GNN-PPO pipeline, and five random seeds.
Results
Compact physical representations led the comparison: Substation achieved 96.7 ± 1.9% episode survival and 99.3±0.5% step survival, while richer representations offered no systematic advantage.
Takeaways & Limitations
Graph construction materially affects learning behavior and robustness, and matching graph complexity to task granularity is more useful than maximizing representational detail.
Takeaways & Limitations
The study is limited to one benchmark, one action set, and one RL architecture.
Abstract
from arXiv · showhide
Graph construction is a critical but underexamined design choice in deep reinforcement learning for power grid control. We present a controlled experimental comparison of different graph representations, including physical topology, electrical-sensitivity, and hybrid variants for topology control in the Learning to Run a Power Network (L2RPN) environment. Our findings indicate that matching graph complexity to task granularity is more important than maximizing representational richness, and highlight the importance of controlled representation studies at scale.
I. INTRODUCTION
Topology control can redirect power flows but is difficult because actions have nonlocal, sequential effects and configurations grow rapidly. The paper isolates graph representation as a design choice in L2RPN topology control.
- Topology reconfiguration redirects power flows by switching lines or changing busbar assignments.
- Topology-action selection is challenging because effects are nonlocal and sequential, while feasible configurations grow rapidly with grid size.
- L2RPN combines time-varying generation and demand with line limits, contingencies, cooldown constraints, and cascading disconnections.
- GNN graph choices determine state granularity, message-passing paths, and computational cost.
- The study compares topology-based, power-flow-based, and hybrid graphs under fixed training and evaluation conditions, with an MLP baseline.
II. RELATED WORK
Prior L2RPN and power-system studies use varied graph abstractions and learning settings. This variation motivates controlled comparisons that isolate observation representation.
- GNN applications in power systems accommodate changing connectivity, but node and edge mappings remain design choices.
- Prior L2RPN agents use default, heterogeneous, and detailed Element physical graph abstractions.
- Different learning and evaluation settings in prior studies prevent controlled comparison of graph representations.
- PTDF, LODF, and bus-impedance quantities provide electrical descriptions complementary to physical adjacency.
III. METHODOLOGY
The methodology compares topology-based, power-flow-based, and hybrid graph representations, defining nodes and edges according to physical connectivity and electrical relations.
- Topology-based graphs define edges from physical grid connectivity.
- Power-flow-based graphs are fully connected and encode electrical sensitivities in edge features.
- Hybrid graphs combine physical and electrical relations using distinct edge types.
- Topology-Based Representations: The Default graph connects line endpoints and elements assigned to the same substation and bus.
- Topology-Based Representations: The Heterogeneous graph distinguishes power-line, same-busbar, and inactive cross-busbar connections.
- Topology-Based Representations: The Substation graph uses active busbars as nodes and power lines between them as edges, whereas the Element graph represents equipment and feasible connections individually.
B. Power-Flow-Based Representations
Power-flow-based representations use fully connected directed graphs whose edge features encode electrical relationships under a DC power-flow approximation. PTDF, LODF, and ZBus graphs differ in node definitions and electrical quantities.
- Power-flow-based graphs use fully connected directed edges with scalar electrical features under a DC power-flow approximation.
- PTDF Graph: PTDF graphs represent active busbars as nodes and use PTDF-based distances between busbars.
- PTDF Graph: PTDF[l, i] measures active-power-flow sensitivity on line l to an injection at busbar i.
- LODF Graph: LODF graphs represent power lines as nodes, with directed edge features equal to the absolute outage-induced flow-transfer factor |LODFij|.
- ZBus Graph: ZBus graphs use active-busbar nodes and impedance-derived coupling weights, where lower impedance indicates stronger electrical coupling.
C. Hybrid representations
Hybrid representations combine topology-based and power-flow-based graphs, distinguishing their relations with separate edge types.
- Each hybrid representation combines a topology-based graph with a power-flow-based graph and assigns the two relations distinct edge types.
- Element + LODF combines the element graph with fully connected LODF edges between power-line nodes.
- Substation + PTDF combines the substation graph with PTDF-distance edges.
- Substation + ZBus retains the same structure as Substation + PTDF but replaces PTDF distances with ZBus coupling weights.
D. GNN Architecture
The shared GNN encoder supports multiple edge types and scalar edge features by using type-specific transformations and feature-derived message weights before graph pooling.
- The encoder uses separate transformation matrices for each edge type and maps scalar edge features to message weights.
- For each node, message passing aggregates information from its neighborhood under each edge type.
- The encoder uses batch normalization, edge-type-specific transformation weights, and degree normalization with self-loops.
- When a representation has no scalar edge features, the edge weight is set to 1.
- After L message-passing layers, mean pooling produces a graph-level embedding that is passed to the same MLP used by the non-graph baseline.
A. Experimental Setup
The study trains graph-based and non-graph PPO agents in the L2RPN case14 sandbox, using a shared evaluation protocol and complementary survival metrics.
- 55 trained runs comprise ten graph representations and a non-graph MLP baseline evaluated across five independent training seeds.
- The MLP receives grid states as a flat vector, while graph-based agents process structured observations with the shared GNN encoder.
- Training uses Proximal Policy Optimization in the l2rpn_case14_sandbox Grid2Op environment for the IEEE 14-bus system.
- Evaluation uses fixed episodes with chronics excluded from training and reports completed episodes and completed evaluation steps.
B. Performance Comparison
Training and held-out performance differ substantially across graph representations. Compact physical graphs perform best overall, while electrical information helps mainly when paired with a weaker physical abstraction.
- The default topology graph converges fastest during training, whereas the Element graph learns more slowly and shows larger late-training declines.
- Substation achieves the highest held-out survival, reaching 96.7 ± 1.9% of episodes and 99.3±0.5% of steps.
- LODF is the strongest standalone electrical representation, while electrical-sensitivity graphs generally remain below the strongest topology-based methods.
- Adding LODF to Element raises episode survival from 86.7% to 92.4% and step survival from 94.3% to 95.9%.
- Across representations, actions concentrate on substations 3, 4, and 8, despite recurring congestion in the 4–5–12 and 3–8–6–7 regions.
- Substation + ZBus results use three successful seeds because two runs failed numerically.
V. CONCLUSIONS
The study finds that graph construction is a consequential design choice, but richer representations do not consistently improve performance. Its conclusions are bounded by evaluation on one benchmark, action set, and RL architecture.
- Ten graph representations and a non-graph MLP were compared under a fixed GNN-PPO pipeline, with every representation supporting a viable policy.
- The compact Substation graph achieves the highest mean survival, while richer physical and standalone PTDF- and ZBus-based graphs offer no systematic advantage.
- Graph construction affects learning efficiency and robustness, but the results do not support maximizing representational detail.
- The study is limited to one benchmark, one action set, and one RL architecture, motivating evaluation across larger and structurally different L2RPN environments.