PF$Δ$: A Benchmark Dataset for Power Flow under Load, Generation, and Topology Variations

TL;DR

PFΔ introduces a comprehensive benchmark dataset for power flow that captures load, generation, and topology variations, enabling rigorous, standardized evaluation of PF solvers and graph neural networks across in- and out-of-distribution regimes and near-infeasibility conditions. The dataset encompasses 859{,}800 solved AC PF instances across six grid sizes, with $N$-$1$/$N$-$2$ perturbations and a dedicated near-infeasibility regime generated via continuation power flow, complemented by a flexible data format and standardized tasks and metrics. Experimental results show that while GNN-based PF solvers can achieve substantial runtime speedups over Newton–Raphson, achieving NR-level accuracy remains an open challenge, especially for larger grids and cross-size generalization; training with topology-diverse data improves generalization, but no model yet matches traditional solvers in all regimes. PFΔ thus provides a crucial platform to benchmark, diagnose, and drive the development of scalable, reliable PF methods suitable for real-time grid operations and planning under high variability and uncertainty.

Abstract

Power flow (PF) calculations are the backbone of real-time grid operations, across workflows such as contingency analysis (where repeated PF evaluations assess grid security under outages) and topology optimization (which involves PF-based searches over combinatorially large action spaces). Running these calculations at operational timescales or across large evaluation spaces remains a major computational bottleneck. Additionally, growing uncertainty in power system operations from the integration of renewables and climate-induced extreme weather also calls for tools that can accurately and efficiently simulate a wide range of scenarios and operating conditions. Machine learning methods offer a potential speedup over traditional solvers, but their performance has not been systematically assessed on benchmarks that capture real-world variability. This paper introduces PF$Δ$, a benchmark dataset for power flow that captures diverse variations in load, generation, and topology. PF$Δ$ contains 859,800 solved power flow instances spanning six different bus system sizes, capturing three types of contingency scenarios (N , N -1, and N -2), and including close-to-infeasible cases near steady-state voltage stability limits. We evaluate traditional solvers and GNN-based methods, highlighting key areas where existing approaches struggle, and identifying open problems for future research. Our dataset is available at https://huggingface.co/datasets/pfdelta/pfdelta/tree/main and our code with data generation scripts and model implementations is at https://github.com/MOSSLab-MIT/pfdelta.

Figures (19)

• Figure 1: Illustration of a generator and load in a power system bus, labeled with each component's associated variables, adapted from Glover2017.
• Figure 2: Bus types and their known (input) and unknown (output) variables in power flow analysis.
• Figure 3: Data generation process for a single data sample within PF$\Delta$.
• Figure 4: Experimental results for all selected tasks.
• Figure 5: Results for Task 3.1 showcasing the Power Balance Loss (PBL) on a combined feasible and close-to-infeasible test set for three bus sizes. Runtimes and PBL of Newton-Raphson (NR) are reported only for the samples of the test set that converged from a flat start. Convergence rates are 95.2%, 65.7%, and 43.4% for bus sizes 57, 118, and 500, respectively, and PBL values for NR were approximately on the order of magnitude of $10^{-6}$. Runtime and PBL values for bus size 2000 are not included as NR failed to converge from a flat start for this system size. NR runtimes were calculated on an Intel Xeon Gold 6140 CPU and GNN runtimes were calculated on an NVDIA RTX 8000 GPU.