Benchmarking Graph Neural Networks for AC Power Flow: The Role of Inductive Biases and Physical Constraints

Federico Clerici; Ferran Bohigas-Daranas; Hamid Latif-Martínez; Eduardo Prieto-Araujo; Oriol Gomis-Bellmunt; Pere Barlet-Ros

cs.LGOct 28, 2026

Benchmarking Graph Neural Networks for AC Power Flow: The Role of Inductive Biases and Physical Constraints

Authors: Federico Clerici, Ferran Bohigas-Daranas, Hamid Latif-Martínez, Eduardo Prieto-Araujo, Oriol Gomis-Bellmunt, Pere Barlet-Ros

Organizations: Universitat Politècnica de Catalunya · BarcelonaTech (UPC), Barcelona, Spain · Department of Mathematics, University of Padua, Padua, Italy · Centre d’Innovació Tecnològica en Convertidors Estàtics i Accionaments (CITCEA-UPC), Universitat Politècnica de Catalunya · BarcelonaTech (UPC), Barcelona, Spain · Barcelona Neural Networking Center (BNN), Universitat Politècnica de Catalunya · BarcelonaTech (UPC), Barcelona, Spain

Abstract

Fast and accurate models for AC power flow (ACPF) are increasingly important as modern electrical grids require more frequent system analyses. Graph neural networks (GNNs) naturally exploit electrical grid topology, yet the effects of architectural design choices on predictive performance remain poorly understood given differences in graph representations and evaluation settings across studies. We present a unified benchmark of representative GNN architectures for ACPF prediction under a common experimental framework. All models use identical preprocessing and training procedures and comparable parameter budgets, isolating the impact of message-passing mechanisms and inductive biases. We also analyze errors by distance from the slack bus and systematically ablate key design components. We evaluate predictive accuracy and physical consistency on the IEEE 14-bus and IEEE 118-bus systems. Results indicate that anisotropic message-passing architectures offer the most favorable trade-off between predictive accuracy and physical consistency under the studied parameter and topology constraints. Explicit edge features encoding line impedances and global context aggregation are particularly important for representing electrical interactions and system-wide dependencies, especially for voltage-angle predictions on the topologically bottlenecked IEEE-118 grid. Under a budget with approximately fixed parameters, two or three message-passing layers generally provide the best balance between depth and representation width, while additional depth offers no consistent improvement. Ablations also show that standard residual and root connections are not necessarily beneficial in shallow models, and that aggregation operators involve trade-offs between statistical accuracy and physical consistency. These results provide practical guidelines for designing graph-based power system models.

Figures & tables

Panel of Figure 1 — Figure 1: Proposed heterogeneous GNN architecture for AC-PF prediction, highlighting the common components.

Grid	$N$	$E$	$\bar{d}$	PV:PQ	Diameter	ASPL	$\lambda_{1}$
IEEE-14	14	20	2.86	0.44	5	2.37	0.182
IEEE-118	118	179	3.03	0.83	14	6.31	0.009

Table 3: Topological properties of the IEEE benchmark grids used in this work.

Bus Type	Known Variables	Unknown Variables	Role
PQ bus	$P$ , $Q$	$V_{m}$ , $V_{a}$	Load bus
PV bus	$P$ , $V_{m}$	$Q$ , $V_{a}$	Generator bus
slack bus 1 1 1 For the slack bus, $P$ and $Q$ are calculated after solving the AC-PF , whereas only $V_{m}$ and $V_{a}$ are specified a priori. Some formulations do not count $P$ and $Q$ as unknown state variables.	$V_{a}$ , $V_{m}$	$P$ , $Q$	Reference bus

Table 4: Classification of buses in a power network according to their known and unknown variables.

Panel of Figure 2 — Figure 2: IEEE-118 – Voltage magnitude TRMAE (%) ( $V_{m}^{PQ}$ ) vs. message-passing depth $T$ . Dashed line indicates the global best value. Error bars denote one standard deviation over four seeds.

Panel of Figure 3 — Figure 3: IEEE-118 – Voltage angle TRMAE (%) vs. message-passing depth $T$ for $V_{a}^{PQ}$ (left) and $V_{a}^{PV}$ (right). Dashed line indicates the global best value per metric. Error bars denote one standard deviation over four seeds.

Panel of Figure 4 — Figure 4: IEEE-118 – KCL mismatch vs. message-passing depth $T$ for active power $P$ (left) and reactive power $Q$ (right). Dashed line indicates the global best value per metric. Error bars denote one standard deviation over four seeds.

Panel of Figure 5 — Figure 5: Performance of the ResGated model relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Panel of Figure 6 — Figure 6: Performance of the ResGated model (baseline vs ablated without global pooling) relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Appendix figures & tables20 assets

Supplementary material from the paper’s appendix.

Appendix

Model	Mode	$T$	Hidden	Params
GCN	Indep.	1	78	100,698
		2	60	99,780
		3	51	101,031
		4	45	101,160
	Shared	–	53	98,739
GAT	Indep.	1	60	98,460

Appendix

Table 7: Unified Parameter Configurations Across Evaluated Architectures. Detailed specifications for all evaluated GNNs and the MLP baseline, showing the message-passing depth (

T

), hidden representation dimensions, and total parameter counts. Hidden dimensions were specifically scaled for each configuration to maintain a tightly controlled capacity budget of approximately 100,000 parameters across both independent and shared weight modes.

Figure 7: IEEE-118 – Voltage angle TRMAE (%) for

V_{a}^{PQ}

(left) and

V_{a}^{PV}

(right) vs. independent message-passing depth

T

, including MLP baseline.

Figure 8: IEEE-118 – Voltage magnitude TRMAE (%) (

V_{m}^{PQ}

) vs. independent message-passing depth

T

, including MLP baseline.

Figure 9: IEEE-118 – KCL mismatch vs. independent message-passing depth

T

for active power

P

(left) and reactive power

Q

(right), including MLP baseline.

Panel of Figure 10 — Figure 10: IEEE-14 – Voltage angle TRMAE (%) for $V_{a}^{PQ}$ (left) and $V_{a}^{PV}$ (right) vs. message-passing depth $T$ .

Figure 11: IEEE-14 – Voltage angle TRMAE (%) for

V_{a}^{PQ}

(left) and

V_{a}^{PV}

(right) vs. independent message-passing depth

T

, including MLP baseline.

Panel of Figure 12 — Figure 12: IEEE-14 – Voltage magnitude TRMAE (%) ( $V_{m}^{PQ}$ ) vs. message-passing depth $T$ .

Figure 13: IEEE-14 – Voltage magnitude TRMAE (%) (

V_{m}^{PQ}

) vs. independent message-passing depth

T

, including MLP baseline.

Panel of Figure 14 — Figure 14: IEEE-14 – KCL mismatch vs. message-passing depth $T$ for active power $P$ (left) and reactive power $Q$ (right).

Figure 15: IEEE-14 – KCL mismatch vs. independent message-passing depth

T

for active power

P

(left) and reactive power

Q

(right), including MLP baseline.

Figure 16: Physical consistency versus prediction accuracy on the IEEE-14 grid. The scatter plots compare active power (

\Delta P

) and reactive power (

\Delta Q

) mismatch against the average TRMAE across bus types. Results show the evaluated GNN architectures across transformation depths

T_{1}

through

T_{4}

under Independent and Shared parameter configurations.

Figure 17: Physical consistency versus prediction accuracy on the IEEE-118 grid. The scatter plots compare active power (

\Delta P

) and reactive power (

\Delta Q

) mismatch against the average TRMAE across bus types. Results show the evaluated GNN architectures across transformation depths

T_{1}

through

T_{4}

under Independent and Shared parameter configurations.

Panel of Figure 18 — Figure 18: Performance of the GCN model relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Panel of Figure 19 — Figure 19: Performance of the GAT model relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Panel of Figure 20 — Figure 20: Performance of the GINE model relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Panel of Figure 21 — Figure 21: Performance of the GraphSAGE model relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Panel of Figure 22 — Figure 22: Performance of the Transformer model relative to hop distance from the slack bus on the IEEE-118 grid ( $T=2$ , Independent layers). Results reflect the mean and variance across multiple seeds.

Panel of Figure 23 — Figure 23: Cumulative spectral energy proportion for $V_{m}$ and $V_{a}$ averaged across buses for the models on the IEEE-118 grid ( $T=2$ , Independent layers).

Figure 24: Eigenvalue spectrum (

\lambda_{k}

) of the admittance-weighted normalized graph Laplacian for the IEEE-118 network.

Panel of Figure 25 — Figure 25: Mean squared GFT residual energy partitioned into low-, mid-, and high-frequency spectral bands for $V_{m}$ and $V_{a}$ . The red bar highlights performance loss when removing global pooling from the ResGated baseline.

Graph Neural Networks

Graph Neural Networks learn from graph-structured data by combining information across connected nodes, edges, and larger structures.

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Solving the alternating current power flow equations in real time is essential for secure grid operation, yet classical Newton-Raphson solvers can be slow under stressed conditions. Existing graph neural networks for power flow are typically trained on a single system and often degrade on different systems. We present PowerModelsGAT-AI, a physics-informed graph attention network that predicts bus voltages and generator injections. The model uses bus-type-aware masking to handle different bus types and balances multiple loss terms, including a power-mismatch penalty, using learned weights. We evaluate the model on 14 benchmark systems (4 to 6,470 buses) and train a unified model on 13 of these under N-2 (two-branch outage) conditions, achieving an average normalized mean absolute error of 0.89% for voltage magnitudes and R^2 > 0.99 for voltage angles. We also show continual learning: when adapting a base model to a new 1,354-bus system, standard fine-tuning causes severe forgetting with error increases exceeding 1000% on base systems, while our experience replay and elastic weight consolidation strategy keeps error increases below 2% and in some cases improves base-system performance. Interpretability analysis shows that learned attention weights correlate with physical branch parameters (susceptance: r = 0.38; thermal limits: r = 0.22), and feature importance analysis supports that the model captures established power flow relationships.

Abstract

Graph Neural Networks

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