Generative modeling approaches often focus on recovering broad statistical characteristics from the training data. In the context of graph generation, this may refer to degree distributions, clustering coefficients, or spectral properties. However, generating usable distribution feeders when detailed feeder models are unavailable requires more than matching generic graph statistics: the sampled topology must also obey electrical compatibility and radiality rules. We therefore formulate feeder synthesis as a constraint-guided graph generation problem and propose the Power-Grid-constrained Discrete Denoising Diffusion model, PG-DiGress, which learns categorical node and edge patterns from feeder data, while respecting domain-specific rules. Specifically, it injects feeder constraints into the reverse diffusion process through soft masks that suppress incompatible edge classes during denoising, followed by a final projection step that rebuilds a connected, rule-compliant feeder graph. We evaluate PG-DiGress using graph-distribution similarity, feeder-rule satisfaction, structural validity, and downstream model construction. Compared with the unconstrained baseline, PG-DiGress increases the strict feeder pass rate from 13.7% to 96.8%. We also successfully convert the generated graphs into executable feeder models for downstream analysis.
Figures & tables
Figure 1. Representative feeder samples generated by (a) unconstrained DiGress and (b) PG-DiGress. The DiGress sample contains two source nodes and therefore violates the single-source feeder requirement despite exhibiting a plausible branching structure. In contrast, the PG-DiGress sample contains a single source and forms a source-connected topology with conductor and transformer assignments consistent with the sampled node attributes. Side-by-side feeder graphs from unconstrained DiGress and PG-DiGress, highlighting the extra source in the unconstrained sample and the single-source rule-compliant structure in the PG-DiGress sample.
Figure 2. Feeder representation and rule system used in this work. Left: representative attributed SMART-DS feeder graphs, with nodes encoding role and phase and edges encoding conductor or transformer connections. Right: local edge-compatibility rules and representative global topology requirements used to define rule-compliant generation. Two-panel figure showing representative attributed SMART-DS feeder graphs and the local edge-compatibility and global topology rules used for rule-compliant generation.
Figure 3. Overview of PG-DiGress. At each reverse diffusion step, a graph transformer (denoiser) predicts categorical node and edge distributions. The predicted node types and phases define a soft mask that re-weights conductor and transformer classes according to local compatibility rules. After denoising, a final projection uses the predicted edge probabilities to build a radial primary backbone, attaches loads, and reconnects remaining components while keeping the sampled node labels fixed. PG-DiGress reverse diffusion pipeline with graph-transformer predictions, a local compatibility mask for edge classes, and a final projection that builds the global feeder structure.
Category
Interpretation
Count
SOURCE
Feeder source node
1,019
LOAD
End-use or building load
15,306
OTHER
Intermediate bus, pole, or junction
18,767
CONDUCTOR
Same-voltage electrical connection
30,455
TRANSFORMER
Primary–secondary voltage transition
3,618
Table 1. Node and active-edge categories in the processed SMART-DS feeder dataset.
Metric
DiGress
Soft mask only
Projection only
PG-DiGress
Within-graph compliance
Mean conductor-edge compliance (%)
89.2
100.0
88.4
100.0
Mean transformer-edge compliance (%)
54.3
99.3
87.5
100.0
Mean source-to-load path compliance (%)
14.3
94.3
96.0
97.1
Graph-level compliance
Single-source compliance (%)
73.4
45.2
92.3
98.9
Table 2. Feeder-rule compliance and ablation results. Within-graph metrics show the mean fraction of compliant edges or loads across generated samples, whereas graph-level metrics show the percentage of complete graphs satisfying each criterion. The strict feeder pass rate requires all six conditions to hold simultaneously. Higher values are better, and the best result in each row is shown in bold.
Statistic
DiGress
PG-DiGress
Number of nodes
0.660
0.480
Average degree
0.003
0.001
Average shortest-path length
0.846
0.663
Diameter
2.350
1.264
Algebraic connectivity
0.009
0.007
S-metric
40.457
32.503
Table 3. 1 -Wasserstein distance between generated and held-out reference feeder distributions. Lower values ↓ indicate better structural fidelity.
Downstream stage
PG-DiGress success rate (%)
Feeder-model construction
100
Electrical-parameter assignment
100
Power-flow execution
99.8
Power-flow convergence
99.3
Table 4. Fraction of evaluated PG-DiGress samples successfully reaching each stage of the downstream feeder-modeling workflow.
Utilities increasingly rely on planning and operational tools to cope with the increased penetrations of distributed energy resources, yet the lack of realistic, openly available datasets remains a major barrier for benchmarking and comparison. Traditional test feeders, and recently proposed large-scale synthetic networks alleviate this issue but are typically based on heuristic rules and do not learn directly from data. This paper proposes a generative framework based on Generative Adversarial Networks (GANs) to create power distribution network layouts using image-based representations. The model is trained on rasterised views of distribution systems and can operate in two modes: an unconditional configuration that learns layout patterns from the training dataset, and conditional configurations that incorporate geographical context such as street maps and the spatial distribution of consumers. The methodology includes dataset preparation from Geographic Information System (GIS) sources, GAN architecture design, and the analysis of training stability and image resolution. Results from three representative cases show that the proposed approach can reproduce the topologies of low (LV), medium (MV) and high voltage (HV) feeders and align generated layouts with underlying geographical structures. At the same time, the study reveals limitations related to training stability, resolution-dependent artefacts and limits, and the absence of explicit electrical constraints. The proposed framework constitutes a data-driven complement to existing synthetic network generation methods, and could be applied to propose distribution network layouts for the electrification of new areas. This would require future extensions towards power flow, electrically validated models.
Juan Manuel Garcia-Perez, Carlos Mateo
School of Engineering (ICAI), Comillas Pontifical University, Spain · Institute for Research in Technology (IIT), School of Engineering (ICAI), Comillas Pontifical University, Spain
Generative modeling of graph-structured data is crucial for tasks ranging from drug discovery to social network simulation. Among these models, denoising diffusion models have achieved great success in graph generation by learning to progressively reverse a process that adds noise to the original graph. However, the standard noise-prediction approach of diffusion models is suboptimal for graph data. The goal for a graph generative model is to learn the clean graphs' topological properties, such as connectivity and degree distribution. Because a diffusion model that predicts noise does not explicitly learn these topological properties, it is challenging for the model to output graphs with the desired structural statistics. To address this challenge, we introduce Direct Graph Flow Matching (DiGFM), a novel graph transformer model guided by two goals: predict clean graphs and improve sampling efficiency. Distinct from the prevailing diffusion approach, DiGFM employs a continuous flow-matching paradigm and integrates direct graph prediction. Specifically, DiGFM maps the prior noise distribution to the clean graph distribution via a multi-step process: the model repeatedly predicts the underlying clean graph, and a transformation is employed to convert the model output to the velocity vector that points in the direction toward the clean graph distribution. This design enables DiGFM to generate high-quality samples using only 2.5% to 15.6% of the steps required by diffusion-based models, which leads to a 5.3x to 257x speedup in wall-clock inference time. Experiments demonstrate that DiGFM outperforms or matches prior state-of-the-art models across general graph benchmarks and molecular datasets, generating graphs with strong adherence to ground-truth structural statistics at significantly faster inference speeds.
Synthetic power-grid scenarios are essential for planning, resilience assessment, contingency analysis, and data-driven power-system applications. Recent synthetic grid generation methods have improved structural realism and operational feasibility by incorporating engineering knowledge through post-generation validation, optimization, or physics-aware generation. However, generated scenarios may still exhibit low AC feasibility and robustness, limiting their practical value for downstream power-system studies. This paper proposes a feasibility-aware distribution-learning framework that learns the AC-operable joint distribution of network topology, branch electrical parameters, and time-varying load profiles. Instead of enforcing feasibility after generation, the proposed framework incorporates AC power-flow convergence and operational constraints into hierarchical diffusion-based distribution learning. This enables the generator itself to produce operationally feasible grid scenarios through efficient diffusion sampling. The hierarchical architecture decomposes the high-dimensional generation task into three engineering-motivated stages: topology and bus-attribute generation, branch-parameter generation conditioned on the generated structure, and load-profile generation conditioned on both network structure and electrical characteristics. Experiments on benchmark systems demonstrate that the proposed framework significantly improves operational feasibility and contingency robustness while maintaining strong statistical fidelity and eliminating optimization-based post-processing.
Chenhan Xiao, Xinyu He, Haoran Li +2
School of Electrical, Computer and Energy Engineering at Arizona State University, USA