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

Yu Qin, Andrew Glaws, Aadil Latif, Ryan King

arXiv:2609.29879v1cs.LG

TL;DR

Matching generic graph statistics does not ensure a usable feeder when electrical compatibility matters. PG-DiGress adds feeder-rule guidance to discrete diffusion, raising strict feeder pass rates while achieving lower structural-distribution distances than unconstrained DiGress.

  • Problem

    Matching generic graph statistics is insufficient for feeder synthesis because generated topologies may still contain incompatible electrical elements.

    Source: §1 · p. 2

  • Method

    PG-DiGress learns categorical feeder patterns and uses soft masks during reverse diffusion to introduce electrical rules.

    Source: §1 · p. 2

  • Results

    The strict feeder pass rate rises from 13.7% to 96.8%, with lower structural-distribution distances than unconstrained DiGress across reported statistics.

    Source: §8 · p. 20, §7 · p. 20

  • Takeaways & Limitations

    PG-DiGress combines improved feeder-rule satisfaction with lower structural-distribution distances across reported statistics.

    Source: §8 · p. 20, §7 · p. 20

    The encoded rules establish categorical and topological consistency, not full operational feasibility.

    Source: §7 · p. 20

Abstract

from arXiv · show

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.

1 Introduction

Feeder synthesis must produce more than statistically plausible graphs: usable topologies must respect electrical compatibility and source-connected radiality. PG-DiGress combines learned categorical patterns with feeder-rule guidance during generation and a final projection.

1 Introduction

  • Generic graph statistics can match while generated feeders still contain incompatible equipment, disconnected loads, or multiple source-to-load paths.Such graphs may not serve as usable feeder topologies.Source: §1 · p. 2
  • PG-DiGress learns categorical node and edge patterns from feeder data while incorporating electrical rules into generation.Soft masks guide conductor and transformer predictions toward local compatibility during reverse diffusion; a final projection constructs the global feeder structure.Source: §1 · p. 2
  • The work evaluates generated feeders using graph statistics, domain-specific rule satisfaction, structural validity, and downstream feeder-model construction.The stated goal is to test whether explicit feeder rules improve compliance and downstream usability.Source: §1 · pp. 2–3
  • The unconstrained DiGress example has two source nodes despite plausible branching, while the PG-DiGress example has one source and a source-connected topology.The PG-DiGress sample also has conductor and transformer assignments consistent with its node attributes.Source: Figure 1 · p. 3

2 Background and Motivation

The background contrasts engineering-based feeder construction with learned graph generation, then motivates discrete diffusion as a way to learn categorical feeder structure while incorporating feeder-specific rules.

2.1 Synthetic Power-System Generation

  • Engineering-based synthetic feeder workflows use geography, demand, design rules, optimization, and equipment choices to determine where service is needed and how it is connected.The paper instead asks whether recurring structure across existing feeders can be learned as a distribution and sampled for alternative topologies.Source: §2.1 · p. 3
  • This work focuses on learning categorical distribution-feeder topology while incorporating phase, voltage-class, conductor, transformer, and radiality rules into generation.The focus is narrower and complementary to work modeling topology alongside continuous attributes and temporal behavior.Source: §2.1 · p. 4

2.2 Learned Graph Generation

  • Graph generation models and samples graphs, but local edge choices collectively determine global properties such as connectivity, cycles, paths, and components.For feeders, whether an edge is admissible also depends on endpoint voltage class and phase configuration.Source: §2.2 · p. 4

2.3 Discrete Graph Diffusion

  • Discrete diffusion corrupts and denoises categorical node and edge labels, matching the discrete roles, phases, and connection types used in feeder graphs.PG-DiGress retains discrete diffusion for learning feeder variation while introducing feeder rules into sampling.Source: §2.3 · pp. 4–5

3 Problem Formulation

The formulation represents feeders as attributed graphs and defines a rule-compliant subset through electrical compatibility and global topology requirements. PG-DiGress targets that subset while preserving learned structural variation and downstream model construction.

3 Problem Formulation

  • The formulation treats feeder synthesis as attributed-graph generation subject to explicit structural and electrical compatibility rules.The representation specifies learned node and edge attributes, and the rules identify usable distribution feeders.Source: §3 · p. 5

3.1 Feeder Graph Representation

  • The graph representation uses categorical node types, phases, and edge labels, including NO_EDGE for candidate node pairs.SOURCE denotes the feeder head, LOAD an end-use load, and OTHER an intermediate component such as a pole or bus.Source: §3.1 · pp. 5–6
  • Node role and phase jointly encode type–phase combinations, and source labels are restricted to primary-side phase classes.This makes source–primary consistency hold by construction; a LOAD may occur on either feeder side.Source: §3.1 · p. 6

3.2 Feeder Rule System

  • These constraints establish structural feeder validity but do not replace downstream power-flow analysis of voltage, current, loading, or losses.The representation models the feeder as an undirected attributed graph; a radial topology can be rooted at the source for downstream analysis.Source: §3.1 · p. 5, §3.2 · p. 6
  • Local compatibility rules require conductors to stay within one voltage class and use a phase shared by both endpoints, while transformers connect primary and secondary systems.The rules encode electrical compatibility conditions.Source: §3.2 · pp. 6–7
  • Global topology rules require a unique source, source-connected components, a tree-shaped primary conductor subgraph, and a unique path from each load to the source.A primary-side load's path crosses no transformer; a secondary-side load's path crosses exactly one.Source: §3.2 · p. 7

3.3 Generation Objective

  • The generation objective is to learn rule-guided sampling that preserves observed structural variation and produces graphs convertible into downstream feeder models.Direct sampling is challenging because local node–edge compatibility and global feeder topology are coupled.Source: §3.3 · p. 8

4 Methodology

PG-DiGress keeps the discrete graph diffusion model’s learned feeder patterns while applying electrical-rule guidance during sampling and global topology repair after denoising. It separates local edge compatibility from global feeder structure, leaving sampled node labels fixed during final projection.

4.1 Discrete Graph Diffusion

  • Discrete diffusion progressively corrupts categorical node and edge labels, then a graph transformer predicts clean-label distributions; the unconstrained baseline does not enforce electrical compatibility or global connectivity and radiality.The node set remains fixed throughout the diffusion trajectory.Source: §4.1 · pp. 9–10

4.2 PG-DiGress: Rule-Guided Sampling

  • PG-DiGress preserves the trained DiGress denoiser and changes edge generation, using node attributes to guide compatible connection classes without redesigning the node generator or retraining.The preliminary guided graph proceeds to final projection.Source: §4.2 · p. 10

4.3 Soft Mask for Local Edge Compatibility

  • A soft mask reweights reverse-step edge probabilities using predicted node types and phases, suppressing illegal conductor and transformer classes while retaining probabilistic sampling.Conductors require equal voltage class and overlapping phases; transformers connect primary and secondary systems.Source: §4.3 · p. 11

4.4 Final Projection for Global Feeder Structure

  • Final projection recomputes compatibility from sampled node labels, builds a radial primary backbone, attaches loads, and reconnects components through legal bridges without changing node labels.The primary backbone is a maximum-weight spanning tree when its legal candidate graph is connected; otherwise, reconnection handles remaining components.Source: §4.4 · pp. 11–13

5 Experiments

The experiments compare PG-DiGress with unconstrained DiGress and ablated variants on feeder-rule compliance, structural fidelity, and downstream model construction. On SMART-DS feeder graphs, the reported strict feeder pass rate rises from 13.7% to 96.8%.

5.1 Dataset

  • The dataset contains 1,019 SMART-DS feeder graphs, split by feeder into disjoint training, validation, and test sets, with held-out feeders used for distributional comparisons.Each feeder is represented as an attributed, undirected graph with semantic node types and phases and categorical connection classes.Source: §5.1 · p. 14

5.2 Implementation Details

  • Training retains categorical node type, phase, and edge type, converts feeders to undirected graphs, and discards continuous attributes.Node type and phase are combined into a categorical node label; an additional NO_EDGE class represents absent edges.Source: §5.2 · p. 14

5.3 Ablation Study

  • Four variants use the same trained denoiser and sampling configuration, isolating edge masking and final projection against unconstrained DiGress.The variants are DiGress, mask only, projection only, and complete PG-DiGress.Source: §5.3 · pp. 14–15

5.4 Evaluation Metrics

  • Evaluation covers feeder-rule compliance, structural distributions against held-out feeders, and sequential feeder-model construction, parameter assignment, power-flow execution, and convergence.Structural metrics include graph scale, sparsity, global extent, connectivity, and degree mixing.Source: §5.4 · pp. 15–16
  • The strict feeder criterion exceeds the model builder’s minimum requirements, while power-flow convergence depends on assigned electrical parameters and operating conditions.Convergence is treated as an operational check under the tested scenario, not a guarantee under arbitrary operating conditions.Source: §5.4 · p. 16
  • Table 2 defines strict feeder pass rate as the percentage of complete graphs satisfying all six conditions simultaneously; higher values are better, and the best result in each row is bolded.Source: Table 2 · p. 17

6 Results

PG-DiGress substantially improves feeder-rule compliance while preserving structural fidelity, and its generated topologies progress to executable feeder models and power-flow analysis.

6.1 Rule Guidance Improves Feeder Compliance

  • The strict feeder pass rate rises from 13.7% to 96.8% with PG-DiGress, an improvement of 83.1 percentage points.Source: §6.1 · p. 17
  • Soft masking raises conductor-edge compliance from 89.2% to 100.0%, transformer-edge compliance from 54.3% to 99.3%, and source-to-load path compliance from 14.3% to 94.3%, but only 42.3% are connected and 27.5% satisfy primary radiality.The strict feeder pass rate is 27.1%, showing that local guidance alone does not impose the required global structure.Source: §6.1 · p. 17
  • Figure 1 contrasts DiGress’s two-source violation with PG-DiGress’s single-source, source-connected topology and compatible assignments, a failure not apparent from graph size or density alone.Source: §6.1 · pp. 17–18

6.2 Rule Guidance Preserves Structural Variation

  • Generated path distributions remain shifted toward shorter average paths and smaller diameters; node-count curves closely match because sizes are sampled from the empirical training distribution.Source: §6.2 · p. 18
  • PG-DiGress has lower 1-Wasserstein distance than DiGress for every reported statistic, including average shortest-path length (0.846 to 0.663), diameter (2.350 to 1.264), and S-metric (40.457 to 32.503).Lower values indicate better structural fidelity.Source: §6.2 · pp. 18–19, Table 3 · p. 19

6.3 Downstream Feeder-Model Construction

  • All evaluated PG-DiGress samples convert into feeder models; 99.8% proceed to power-flow execution and 99.3% converge.Source: §6.3 · p. 19, Table 4 · p. 19
  • Power-flow convergence is an operational check, not proof of feasibility under all loading, voltage, thermal, protection, or contingency conditions.Source: §6.3 · p. 19

7 Discussion

PG-DiGress combines local edge guidance with a probability-ranked projection to improve feeder-rule compliance while retaining learned structural variation. Its results are stronger on feeder compliance and structural-distribution distances than DiGress, but generated feeders remain more compact than SMART-DS references in path length and diameter.

7 Discussion

  • The soft edge mask guides local compatibility, while projection uses learned edge probabilities to resolve connectivity, radiality, and source-to-load structure.Projection ranks admissible connections rather than replacing learned generation with a fully rule-based construction procedure.Source: §7 · p. 20
  • Structural-distribution similarity and feeder-rule compliance are complementary checks because generic graph statistics miss rule violations and rule repair may alter graph structure.Examples of violations include incompatible edge classes, multiple sources, and invalid source-to-load paths.Source: §7 · p. 20
  • PG-DiGress substantially improves strict feeder pass rate while achieving lower 1-Wasserstein distances than DiGress across all reported structural statistics.The generated feeders nevertheless remain more compact than SMART-DS references in path length and diameter.Source: §7 · p. 20
  • PG-DiGress modifies edge generation only; sampled node types and phase labels mean it cannot directly repair invalid source counts or inconsistent node attributes.The encoded rules establish categorical and topological consistency, not full operational feasibility; voltage, loading, losses, and related outcomes require parameter assignment and explicit simulation.Source: §7 · p. 20
  • The learned distribution is limited to SMART-DS feeders and this categorical representation, so transferability across regions, feeder sizes, utilities, and construction procedures remains to be assessed.The paper identifies evaluation on those additional settings as necessary to assess transferability beyond this dataset.Source: §7 · p. 20
  • Future work could extend rule guidance to node attributes, condition generation on partial topology or external context, and incorporate power-flow or resilience feedback.These extensions are proposed as steps toward feeder completion and conditional, operationally informed distribution-system synthesis.Source: §7 · p. 20

8 Conclusion

PG-DiGress applies soft compatibility masks during reverse diffusion and projects samples into a global feeder structure. On SMART-DS graphs, it improves strict feeder pass rate and structural-distribution distances versus unconstrained DiGress, and generated topologies support feeder-model construction and power-flow execution.

8 Conclusion

  • PG-DiGress retains standard DiGress training, guides local edge sampling with a soft compatibility mask, and projects samples into the final global feeder structure.The projection uses learned edge probabilities to construct the structure.Source: §8 · p. 20
  • On SMART-DS feeder graphs, PG-DiGress increases the strict feeder pass rate from 13.7% to 96.8% and achieves lower structural-distribution distances than unconstrained DiGress across all reported statistics.The generated topologies also support downstream feeder-model construction and power-flow execution.Source: §8 · p. 20
  • The method improves edge compatibility and topology conditional on sampled node attributes, but does not guarantee valid node labels or operational power-flow feasibility.The conclusion identifies node-generation rule guidance and electrical simulation feedback as steps toward conditional, operationally informed synthesis.Source: §8 · pp. 20–21

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