cs.LGSep 24, 2026

From Graphs to Feeders: Constraint-Guided Diffusion for Rule-Compliant Feeder Generation

Authors: Yu Qin, Andrew Glaws, Aadil Latif, Ryan King

Organizations: National Laboratory of the Rockies, Golden, Colorado, USA

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Abstract

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.
CategoryInterpretationCount
SOURCEFeeder source node1,019
LOADEnd-use or building load15,306
OTHERIntermediate bus, pole, or junction18,767
CONDUCTORSame-voltage electrical connection30,455
TRANSFORMERPrimary–secondary voltage transition3,618
Table 1. Node and active-edge categories in the processed SMART-DS feeder dataset.
MetricDiGressSoft mask onlyProjection onlyPG-DiGress
Within-graph compliance
Mean conductor-edge compliance (%)89.2100.088.4100.0
Mean transformer-edge compliance (%)54.399.387.5100.0
Mean source-to-load path compliance (%)14.394.396.097.1
Graph-level compliance
Single-source compliance (%)73.445.292.398.9
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.
StatisticDiGressPG-DiGress
Number of nodes0.6600.480
Average degree0.0030.001
Average shortest-path length0.8460.663
Diameter2.3501.264
Algebraic connectivity0.0090.007
S-metric40.45732.503
Table 3. 11 -Wasserstein distance between generated and held-out reference feeder distributions. Lower values ↓\downarrow indicate better structural fidelity.
Downstream stagePG-DiGress success rate (%)
Feeder-model construction100
Electrical-parameter assignment100
Power-flow execution99.8
Power-flow convergence99.3
Table 4. Fraction of evaluated PG-DiGress samples successfully reaching each stage of the downstream feeder-modeling workflow.

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