A graph-based artificial-intelligence model called UNION reported a 1.20% average gap from reference operating costs across 14,000 held-out normal-operation instances spanning seven AC-OPF systems. Its average constraint-satisfaction ratio, or CSR, was 99.73%; after deterministic restoration, the average gap was 1.23% and strict feasibility was 99.56%.
AC-OPF is a problem of setting generator controls while respecting network constraints. The paper asks whether one jointly trained model can produce feasible, low-cost solutions across heterogeneous systems and changing active topologies.
How the model fills in the network state
The reported training setup used one shared model across seven systems. UNION combines a shared graph encoder, scalar-gated aggregation with explicit consensus correction, a sparse-aware differentiable implicit AC power-flow layer, primal-dual training and deterministic restoration.
For an unseen operating configuration, the model predicts generator-control setpoints and solves the nonlinear AC power-flow equations for the active topology. The dependent electrical state is completed for the topology being tested rather than having the full operating point extrapolated by the graph model alone.
The benchmark and its tests
Demand in the benchmark was perturbed by up to 10% above or below nominal values. Each of the seven systems had 1,000 training instances, 1,000 validation instances and 2,000 test instances.
Normal operation was evaluated on all seven systems. Four representative systems also received selected zero-shot N−1 tests, meaning a single line or generator outage at a time, and a separate temporal evaluation used 116 hourly Korea-4492 snapshots over five days.
The contingency evaluation sampled 20 line outages and up to 10 eligible non-reference generator outages per system, with 1,000 load instances for each contingency.
Strong results in normal operation
Across the normal held-out set, UNION had the lowest reported average pre-restoration objective gap among compared methods and the highest average CSR: 1.20% and 99.73%, respectively. After restoration, six systems had 100% strict feasibility and GOC-2312 had 96.95%, producing an average post-restoration strict-feasibility rate of 99.56%; the average post-restoration objective gap was 1.23%.
Outages and time-series tests
On selected zero-shot outage tests, UNION recorded 100% post-restoration strict feasibility on GOC-4601 and Korea-4492 for both line and generator outage types. The reported post-restoration objective gaps in those tests ranged from 0.24% to 0.93%.
In the Korea-4492 temporal test, zero-shot UNION coverage was 92.24% across the 116 hourly snapshots. The online fine-tuned condition covered 100% of snapshots and reported a 2.51% post-restoration objective gap, with an 82.8% post-restoration strict-feasibility rate.
Those temporal quality figures were calculated only on snapshots with complete power-flow-consistent inference: GapR, CSR and IFRR were conditional on coverage. Coverage and the reported metrics therefore need to be read together.
The paper reports that some uncovered zero-shot cases had predicted active-power dispatch that could not be balanced within the available reference-generator range. The power-flow solve did not converge in those cases, so the restoration step was blocked.
Aggregation variants and timing
An ablation averaged results equally across seven systems for two aggregation configurations. SGA+ECC recorded a 1.19% pre-restoration Gap and 99.74% CSR, compared with 1.43% Gap and 99.65% CSR for SGA without ECC.
At batch size one on the three largest systems, sparse-aware implicit inference took 55 to 58 milliseconds per instance, while the full UNION pipeline took 108 to 114 milliseconds. The paper reports a 4.1- to 4.5-fold speedup over the dense implicit layer under that setup.
UNION was trained with validation-based checkpoint selection over at most 7,000 epochs. Adam used a batch size of 16 and a learning rate of 10−3, and the full run took 175 hours on one NVIDIA GeForce RTX 4090 GPU.
The tested boundary
The evidence remains tied to the tested computational settings: seven systems in normal operation, selected outage sets on four representative systems and 116 hourly snapshots over five days. The contingency results came from a selected sample rather than an exhaustive outage set.
The document is an arXiv v1 preprint dated 26 August 2026 and says it was submitted to the IEEE for possible publication.
The work was supported by the National Research Foundation of Korea under Grant RS-2025-02215243 and the Korea Institute of Energy Technology Evaluation and Planning under Grant RS-2026-25527712.
Paper data and sources
Original title: UNION: A Unified AC-OPF Framework for Topology-Varying Real-Time Grid Operation
Authors: Kyungnam Park, Keunju Song, Yeji Lim et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text