Towards Hierarchical GNNs for multi-grid power flow: generalization across operating scenarios

Hierarchical latent communication improves the generalization of a multi-grid power-flow model to new operating scenarios. The module exchanges information through two reduced graphs within a GENCO-based corrective network. We compare Kron-derived transports, a same-anchor Quotient construction and a flat backbone in preliminary trainings of 200 epochs on three grid topologies, with three initialization seeds per model. Evaluation uses 200 newly generated, preselected scenarios per grid. On the training topologies, Kron reduces the macro family-balanced voltage error from 5.660 +- 0.899 to 0.851 +- 0.110: an 85.0% reduction relative to Flat GENCO and 31.0% relative to Quotient, which reaches 1.235 +- 0.225. Both hierarchical models outperform a per-bus mean fitted on training solutions on every training topology in all three seeds. These results demonstrate generalization across operating scenarios within the studied topologies, with one set of learned parameters shared across grids. Evaluation on two additional topologies distinguishes this achievement from cross-topology generalization: the current models do not yet outperform the fitted reference in that calibrated- transfer setting. This preprint presents the architecture and preliminary evidence for hierarchical communication as a component of multi-grid power-flow learning, with generalization to unseen topologies as the next development objective.