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Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator

Changhun Kim, Timon Conrad, Redwanul Karim, Julian Oelhaf, David Riebesel, Tomás Arias-Vergara, Andreas Maier, Johann Jäger, Siming Bayer

TL;DR

Addresses the need for fast, accurate AC power-flow solutions across large scenario sets by combining physics-informed learning with graph attention. The approach introduces PIGNN-Attn-LS, a physics-informed graph neural network that uses edge-aware attention and a backtracking line-search-based correction operator, trained without Newton-Raphson supervision. It achieves NR-level accuracy on HV and MV grids, with voltage RMSE around 0.00033 p.u. and angle errors near 0.08 degrees, while delivering 2–5x inference speedups and scaling to grids up to 1024 buses. This work demonstrates the practicality of physics-informed, graph-based solvers for operational planning and security assessment in power systems.

Abstract

Physics-informed graph neural networks (PIGNNs) have emerged as fast AC power-flow solvers that can replace the classic NewtonRaphson (NR) solvers, especially when thousands of scenarios must be evaluated. However, current PIGNNs still need accuracy improvements at parity speed; in particular, the soft constraint on the physics loss is inoperative at inference, which can deter operational adoption. We address this with PIGNN-Attn-LS, combining an edge-aware attention mechanism that explicitly encodes line physics via per-edge biases to form a fully differentiable knownoperator layer inside the computation graph, with a backtracking line-search-based globalized correction operator that restores an operative decrease criterion at inference. Training and testing use a realistic High-/Medium-Voltage scenario generator, with NR used only to construct reference states. On held-out HV cases consisting of 4-32-bus grids, PIGNN-Attn-LS achieves a test RMSE of 0.00033 p.u. in voltage and 0.08 deg in angle, outperforming the PIGNN-MLP baseline by 99.5% and 87.1%, respectively. With streaming micro-batches, it delivers 2-5x faster batched inference than NR on 4-1024-bus grids.

Physics-informed GNN for medium-high voltage AC power flow with edge-aware attention and line search correction operator

TL;DR

Addresses the need for fast, accurate AC power-flow solutions across large scenario sets by combining physics-informed learning with graph attention. The approach introduces PIGNN-Attn-LS, a physics-informed graph neural network that uses edge-aware attention and a backtracking line-search-based correction operator, trained without Newton-Raphson supervision. It achieves NR-level accuracy on HV and MV grids, with voltage RMSE around 0.00033 p.u. and angle errors near 0.08 degrees, while delivering 2–5x inference speedups and scaling to grids up to 1024 buses. This work demonstrates the practicality of physics-informed, graph-based solvers for operational planning and security assessment in power systems.

Abstract

Physics-informed graph neural networks (PIGNNs) have emerged as fast AC power-flow solvers that can replace the classic NewtonRaphson (NR) solvers, especially when thousands of scenarios must be evaluated. However, current PIGNNs still need accuracy improvements at parity speed; in particular, the soft constraint on the physics loss is inoperative at inference, which can deter operational adoption. We address this with PIGNN-Attn-LS, combining an edge-aware attention mechanism that explicitly encodes line physics via per-edge biases to form a fully differentiable knownoperator layer inside the computation graph, with a backtracking line-search-based globalized correction operator that restores an operative decrease criterion at inference. Training and testing use a realistic High-/Medium-Voltage scenario generator, with NR used only to construct reference states. On held-out HV cases consisting of 4-32-bus grids, PIGNN-Attn-LS achieves a test RMSE of 0.00033 p.u. in voltage and 0.08 deg in angle, outperforming the PIGNN-MLP baseline by 99.5% and 87.1%, respectively. With streaming micro-batches, it delivers 2-5x faster batched inference than NR on 4-1024-bus grids.

Paper Structure

This paper contains 12 sections, 8 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Problem Formulation
  4. Unrolling $K$ Correction Steps
  5. Physics-Informed, Edge-Aware Multi-Head Self-Attention
  6. Backtracking line search and Voltage update caps
  7. Scenario Synthesis and Reference Power-Flow Solutions (MV & HV)
  8. Experiments and Results
  9. Data Preprocessing and Implementation Details
  10. Ablation Studies
  11. Throughput
  12. Conclusion

Figures (3)

  • Figure 1: Architecture of PIGNN-Attn-LS. Message aggregation uses L layers of edge-aware multi-head self-attention and is interchangeable with an MLP. The central node denotes the bus of interest; incoming edges are weighted by attention scores, with lower opacity indicating lower importance.
  • Figure 2: Three-bus $\pi$-model (series $R{+}jX$; half shunt per line end). $Z_{ij}=(R'+jX')L_{ij}$, $y_{ij}=1/Z_{ij}$, $B^{\mathrm{sh}}_{ij}=\omega C' L_{ij}$ (total per line, split as $B^{\mathrm{sh}}_{ij}/2$ at each end); $B^{\mathrm{sh}}_{i}=\tfrac{1}{2}\!\sum_{j\in\mathcal{N}(i)}\!B^{\mathrm{sh}}_{ij}$. Admittance matrix: $Y_{ij}=-y_{ij}$ on lines and $Y_{ii}=\sum_{k\in\mathcal{N}(i)} y_{ik}+\jmath B^{\mathrm{sh}}_{i}$.
  • Figure 3: Computational time over grid size for NR and PIGNN variants. Results are reported as median inference time (over multiple runs with 2 warmup and 5 repeat cycles).