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PF∆: A Benchmark Dataset for Power Flow under Load, Generation, and Topology Variations
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Introduces PFΔ, a benchmark of 859,800 AC power flow instances across six bus systems with load, generator, and N-1/N-2 topology perturbations plus close-to-infeasible cases, and benchmarks Newton-Raphson against three GNN solvers.
Problem
Machine learning power flow solvers lack standardized benchmarks that capture load, generation, and topology variability, including near-infeasible operating points near voltage stability limits.
Approach
A data generation pipeline that jointly perturbs loads (OPF-Learn sampling), generator cost-driven setpoints, and N/N-1/N-2 topologies, plus close-to-infeasible cases from continuation power flow, with unsupervised power-balance metrics for evaluation.
Key results
- Newton-Raphson achieves power balance loss around 1e-6, while no GNN model reaches comparable precision on IEEE-118 tasks.
- The fastest GNN model achieves approximately a 5x speedup over Newton-Raphson runtime on larger grids, but all three GNNs struggle to generalize to different grid sizes.
- Training on N-1 perturbations improves generalization to both N-1 and N-2 cases across all GNN models; models trained only on N topology perform poorly on perturbed topologies.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train on N-1 topological perturbations rather than only the base N topology | CANOS-PF, PFNet, and GNS-S · In-distribution N-1 and N-2 cases | power balance loss | Helped |
| Add approaching-infeasible cases to training (ablation) | CANOS-PF · Close-to-infeasible cases, Task 4.2 | power balance loss | Helped |
| Train on close-to-infeasible and approaching-infeasible cases only (ablation) | Task 4.3 models · Close-to-infeasible cases | power balance loss | Helped |
| Train only on close-to-infeasible and approaching-infeasible cases instead of including feasible cases (ablation) | Task 4.3 models · Feasible cases | power balance loss | Hurt |
| Train only on close-to-infeasible and approaching-infeasible cases (ablation) | CANOS-PF and GNS-S · Feasible cases, Task 4.3 | power balance loss | No clear effect |
| Train only on close-to-infeasible and approaching-infeasible cases (ablation) | PFNet · Feasible cases, Task 4.3 | power balance loss | Hurt |
| Train on N topology only, without topological perturbations (ablation) | GNS-S · Low-data regime | power balance loss | Hurt |
| Evaluate GNN-based models instead of Newton-Raphson | CANOS-PF, PowerFlowNet, and GNS-S · Runtime across tested grid sizes | runtime: approximately a 5$\times$ speedup | Helped |
| Train on one grid size and evaluate on different grid sizes | CANOS-PF, PowerFlowNet, and GNS-S · Out-of-distribution grid sizes | power balance loss | Hurt |
| Use supervised learning without the physics-informed components | PowerFlowNet · Close-to-infeasible cases | power balance loss | Hurt |
| Train without close-to-infeasible samples | Models evaluated on close-to-infeasible cases · Close-to-infeasible cases | power balance loss | Hurt |
Surprising findings
- Models trained only on the base topology perform poorly on N-1 and N-2 cases, even CANOS-PF, the best average performer.
- PFNet's performance drops drastically when trained only on near-infeasible samples, while CANOS-PF and GNS-S retain feasible-case accuracy.
Limitations
- GNN models do not reach Newton-Raphson-level power balance precision (~1e-6).
- All tested GNNs struggle to generalize to grid sizes different from the training grid.
- GOC-2000 has fewer samples (61,800) due to computational cost, and NR fails to converge from flat start on it.
Experimental setup
Datasets: PFΔ
Benchmarks: PFΔ
Metrics: mean power balance loss max power balance loss solver runtime interpretability statistics on nodal features
Baselines: Newton-Raphson CANOS-PF PowerFlowNet GraphNeuralSolver
Builds on: OPF-Learn PowerModels.jl MATPOWER continuation power flow
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