'''Generative Models for Medium-Voltage Subgrids: Synthetic Data Augmentation for Distribution-Grid AI ''' Embedded in: Alliander–Radboud collaboration on distribution-grid AI, building on GNN grid-reliability work (Cambier van Nooten et al., 2025).
Supervisors: Dr. Yuliya Shapovalova (Radboud); Gerson Foks (Alliander).
Duration: 6 months.
1. Context and motivation
Alliander's medium-voltage grid contains tens of thousands of nodes and edges. For most modelling tasks it is sliced into roughly 180 feeder- or substation-level subgrids, each consisting of one substation and multiple middenspanningsruimtes (MS rooms). That sample size is the core bottleneck for data-driven methods: modern graph neural networks are typically trained on datasets one to three orders of magnitude larger, and recent empirical work reports that even well-tuned graph VAEs struggle on hundreds-to-thousands of realistic feeders, producing disconnected components and repeated motifs on the more complex open benchmarks (Exploring VGAEs for Distribution Grid Data Generation, 2025). Two things change if we can generate representative synthetic subgrids. First, downstream AI tasks (n-1 reliability assessment [Cambier van Nooten et al., 2025], load-flow surrogates, state estimation, data correction) become tractable with larger, better-mixed training sets. Second, because real grid topology is confidential, a high-quality generator opens a realistic sharing channel with academic partners: students and research groups can work on representative data without access to the real network. An internal intern project at Alliander made an early attempt at generative subgrid modelling but was constrained by data availability; the field has moved substantially since (DiGress and diffusion-based graph generators in 2023–2024; dedicated power-grid generators such as FeederGAN and DeepGDL), so a focused revisit is well-timed. (This is the graph-generation counterpart to the other Alliander graph thesis on learning geographical routing constraints; the two are complementary but independent.)
2. Objective and research questions
Main question: can a deep generative model, trained on Alliander's ~180 real subgrids (augmented with rule-based synthetic data), produce medium-voltage subgrids that are simultaneously 1) statistically representative of the real population, 2) diverse rather than memorised, and 3) useful as augmentation data for downstream grid-AI tasks?
- RQ1 (Fidelity and diversity in the small-data regime). Which class of graph generative model — autoregressive (GraphRNN-style), one-shot adversarial (FeederGAN-style), latent-variable (VGAE / DeepGDL), or denoising-diffusion (DiGress) — best balances statistical fidelity against sample diversity when trained on ~180 real subgrids plus rule-based synthetic data? Pretraining on the rule-based generator and fine-tuning on real data is tested as a transfer strategy.
- RQ2 (Domain constraints). How much does adding power-grid-specific structural priors (radiality / tree structure per feeder, connectivity, expected average node degree, substation counts) to the loss or architecture improve sample validity, compared to a purely data-driven generator? Approaches include soft penalties, post-hoc rejection sampling, and constrained decoders.
- RQ3 (Downstream usefulness). Does augmenting the training set with generated subgrids improve performance on a concrete downstream task — n-1 contingency prediction using the GIN of Cambier van Nooten et al. (2025) and at what mixing ratio of real to synthetic data? This is the decisive test: a generator that produces pretty-looking graphs but does not help downstream tasks has not succeeded. Optional stretch directions (chosen with the supervisor after baseline results): conditional generation (size, substation type, region); inclusion of node and edge attributes (coordinates, cable type, lengths) alongside topology; and joint generation of topology and operating conditions following PowerGrow (2025).
3. Background: state of the art
Graph generation spans four families (Guo & Zhao, 2022): autoregressive models (GraphRNN), one-shot adversarial models, latent-variable models (VGAE), and denoising-diffusion models (DiGress, current state of the art on non-molecular graphs, supporting categorical node/edge attributes and conditional generation). For power grids specifically, dedicated generators include FeederGAN (adversarial, designed for distribution feeders) and DeepGDL (Khodayar et al., 2019, a recurrent graph-distribution learner). A recent VGAE study (2025) documents the small-data failure modes this thesis must overcome, and PowerGrow (2025) extends generation to joint topology-and-dynamics. The gap: none of these is validated in a ~180-graph small-data regime with a downstream-utility test.
4. Proposed approach
Data. Roughly 180 real Alliander medium-voltage subgrids (one substation + multiple MS rooms each) plus an internal rule-based generator that produces less-representative synthetic subgrids in unlimited quantity.
Models (baseline → advanced), following Guo & Zhao (2022). Autoregressive baseline: GraphRNN (You et al., 2018) — a well-understood reference that scales to hundreds of nodes with widely-used benchmark metrics. Domain-tailored adversarial baseline: FeederGAN (Liang et al., 2021), the closest published work, designed for distribution feeders. Latent-variable baseline: a VGAE, following the recent distribution-grid VGAE study (2025) and the earlier DeepGDL generator (Khodayar et al., 2019), a natural starting point when sample counts are small. Advanced model: DiGress (Vignac et al., 2023), discrete denoising diffusion, current state of the art on non-molecular graphs. Training strategy. The rule-based generator is used both for pretraining with domain adaptation to real data, and for creating a larger controlled benchmark on which models can be debugged before training on the scarce real set. Cross-validation uses leave-out groups of subgrids rather than random splits.
Evaluation (four complementary layers). 1) Distributional fidelity: Maximum Mean Discrepancy on degree, clustering, orbit, and spectral distributions (the GraphRNN benchmark), plus MMD on node/edge-attribute distributions. 2) Domain validity: the rate of generated subgrids that are connected, radial, have plausible feeder depth, and match expected substation/MS-room cardinalities ("did it generate a believable grid?"). 3) Downstream utility: train the n-1 GIN (Cambier van Nooten et al., 2025) on real-only vs. real + synthetic data and measure held-out accuracy as a function of the mixing ratio; this is the evaluation the generative-modelling literature often skips. 4) Diversity vs. memorisation: nearest-neighbour distance (graph-edit-distance or WL-kernel) between each generated sample and its nearest training graph, to confirm the model is not copying the 180 real graphs.
5. Deliverables and student profile
Deliverables (examples, can be adjusted): 1) a comparison of graph generative models (GraphRNN / FeederGAN / VGAE / DiGress) for MV-subgrid generation in the small-data regime; 2) a four-layer evaluation (distributional fidelity, domain validity, downstream utility, diversity/memorisation); 3) the decisive downstream result whether synthetic augmentation improves the n-1 GIN, and at what real-to-synthetic mixing ratio; (4) a thesis and code release, optionally with a set of shareable synthetic subgrids.
Contact
Interested? Contact Dr. Yuliya Shapovalova — yuliya.shapovalova@ru.nl — or Gerson Foks (Alliander) — gerson.foks@alliander.com
References
1. Guo, X., & Zhao, L. (2022). A Systematic Survey on Deep Generative Models for Graph Generation. *IEEE Transactions on Pattern Analysis and Machine Intelligence*. arXiv:2007.06686.
2. Liang, M., Meng, Y., Wang, J., Lubkeman, D. L., & Lu, N. (2021). FeederGAN: Synthetic Feeder Generation via Deep Graph Adversarial Nets. *IEEE Transactions on Smart Grid*, 12(2), 1163–1173.
3. Vignac, C., Krawczuk, I., Siraudin, A., Wang, B., Cevher, V., & Frossard, P. (2023). DiGress: Discrete Denoising Diffusion for Graph Generation. *ICLR 2023*. arXiv:2209.14734.
4. You, J., Ying, R., Ren, X., Hamilton, W. L., & Leskovec, J. (2018). GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models. *ICML 2018*. arXiv:1802.08773.
5. Cambier van Nooten, C., van de Poll, T., Füllhase, S., Heres, J., Heskes, T., & Shapovalova, Y. (2025). Graph neural networks for assessing the reliability of the medium-voltage grid. *Applied Energy*, 384, 125401.
6. Abbas, S. Z., & Okoyomon, E. (2025). Exploring Variational Graph Autoencoders for Distribution Grid Data Generation. *NeurIPS 2025*. arXiv:2509.02469.
7. He, X., Xiao, C., Li, H., Qiu, R., Xu, Z., Weng, Y., He, J., & Tong, H. (2025). PowerGrow: Feasible Co-Growth of Structures and Dynamics for Power Grid Synthesis. arXiv:2509.12212.
8. Khodayar, M., Wang, J., & Wang, Z. (2019). Deep Generative Graph Distribution Learning for Synthetic Power Grids (DeepGDL). arXiv:1901.09674.