  The application of graph neural networks (GNNs) to the domain of electrical
power grids has high potential impact on smart grid monitoring. Even though
there is a natural correspondence of power flow to message-passing in GNNs,
their performance on power grids is not well-understood. We argue that there is
a gap between GNN research driven by benchmarks which contain graphs that
differ from power grids in several important aspects. Additionally, inductive
learning of GNNs across multiple power grid topologies has not been explored
with real-world data. We address this gap by means of (i) defining power grid
graph datasets in inductive settings, (ii) an exploratory analysis of graph
properties, and (iii) an empirical study of the concrete learning task of state
estimation on real-world power grids. Our results show that GNNs are more
robust to noise with up to 400% lower error compared to baselines. Furthermore,
due to the unique properties of electrical grids, we do not observe the well
known over-smoothing phenomenon of GNNs and find the best performing models to
be exceptionally deep with up to 13 layers. This is in stark contrast to
existing benchmark datasets where the consensus is that 2 to 3 layer GNNs
perform best. Our results demonstrate that a key challenge in this domain is to
effectively handle long-range dependence.
