Accurate AC power flow (AC-PF) prediction under domain shift is critical when models trained on medium-voltage (MV) grids are deployed on high-voltage (HV) networks. Existing physics-informed graph neural network (GNN) solvers typically rely on full fine-tuning for cross-regime transfer, incurring high retraining cost and offering limited control over the stability-plasticity trade-off between target-domain adaptation and source-domain retention. We study parameter-efficient domain adaptation for physics-informed self-attention-based GNNs, encouraging Kirchhoff-consistent behavior via a physics-based loss while restricting adaptation to low-rank updates. Specifically, we apply low-rank adaptation (LoRA) to attention projections with selective unfreezing of the prediction head to regulate adaptation capacity. This design yields a controllable efficiency-accuracy trade-off for physics-constrained inverse estimation under voltage-regime shift. Across multiple grid topologies, the proposed LoRA+PHead adaptation recovers near-full fine-tuning accuracy with a target-domain RMSE gap of 2.6×10−4 while reducing the number of trainable parameters by 85.46%. The physics-based residual remains comparable to full fine-tuning; however, relative to Full FT, LoRA+PHead reduces MV source retention by 4.7 percentage points (17.9% vs. 22.6%) under domain shift, while still enabling parameter-efficient and physically consistent AC-PF estimation.
Figures & tables
TABLE I : Cross-regime AC-PF prediction performance (MV → HV). Method Prediction Accuracy Efficiency RMSE all↓ RMSE V ↓ RMSE θ ( ∘ ) ↓LPF↓Preduced (%) ↑Rret (%) ↑ ZeroShot (Base) 1.65×10−21.71×10−39.38×10−12.57 — — Full FT 9.35×10−43.61×10−44.95×10−21.110%22.6% Head-only 1.38×10−3‡4.19×10−4‡7.51×10−2‡1.11‡88.50%22.3% LoRA-only 3.61×10−31.05×10−31.98×10−16.0896.56%17.3% LoRA+PHead 1.20×10−3‡3.53×10−4‡6.56×10−2‡1.21‡85.46%17.9% Best results are in bold . ↓↑ indicates lower/higher is better. RMSE: Root Mean Square Error. LPF : Physics-informed PF loss. Preduced : Parameter reduction vs. Full FT. Rret : MV retention, defined as Rret=100⋅RMSEMVmeth/RMSEMVbase . ‡p<0.01 (paired Wilcoxon vs. Full FT over Nwilcox=500 ).
TABLE II : MV/HV parameter ranges. Parameter (unit) MV HV Base voltage (kV) 10 110 Base power (MVA) 10 100 Line length (km) 1–20 1–50 Series resistance ( Ω /km) 0.5–0.6 0.15–0.20 Series reactance ( Ω /km) 0.30–0.35 0.35–0.45 Shunt capacitance (nF/km) 8–14 8–10 Active power (MW) [−5,5][−300,300] Reactive power (MVAr) [−2,2][−150,150] MV/HV experimental setup: Each graph has 4–32 buses; datasets contain 90,030 (MV) and 45,030 (HV) samples; Train/Val/Test split 1:1:1
Table 1
Fig. 1 : Cross-regime adaptation (MV → HV): few-shot scaling, efficiency–accuracy trade-off, and physics-loss dynamics for full fine-tuning and parameter-efficient adaptation.
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.
Changhun Kim, Timon Conrad, Redwanul Karim +6
Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany
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.
Chidozie Ezeakunne, Jose E. Tabarez, Reeju Pokharel +1
Los Alamos National Laboratory, Los Alamos, NM, USA · Department of Physics, University of Central Florida, Orlando, FL 32816 USA
Recent neural power-flow solvers, including emerging foundation models, achieve accurate voltage predictions, yet such accuracy does not necessarily imply physically consistent solutions. Even small complex voltage errors can yield large AC power-balance residuals. We study this accuracy-consistency gap across PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA on realistic 2224-bus Great Britain network (GBnetwork) scenarios, with cross-grid evaluation of GridSFM over 31 systems. Using a singular value decomposition (SVD) basis fitted to training AC power-flow solutions, we find that neural prediction errors contain substantial components outside the dominant solution subspace. To address this mismatch, calibrated solution-subspace projection (CSP) suppresses off-subspace prediction components after train-only bias calibration, reducing Mean PB by 67.0%, 37.8%, 40.5%, and 68.9% for PIGNN-GC, GridSFM, gridfm-graphkit, and LUMINA, respectively, relative to calibrated predictions, while improving voltage-magnitude accuracy in all four models. These results identify output-error geometry as an important factor in physics-consistent neural AC power flow. Code: https://github.com/Kimchangheon/neural-acpf-error-geometry
Changhun Kim, Timon Conrad, Redwanul Karim +7
Pattern Recognition Lab, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany · Institute of Electrical Energy Systems, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany