  The transition away from carbon-based energy sources poses several challenges
for the operation of electricity distribution systems. Increasing shares of
distributed energy resources (e.g. renewable energy generators, electric
vehicles) and internet-connected sensing and control devices (e.g. smart
heating and cooling) require new tools to support accurate, datadriven decision
making. Modelling the effect of such growing complexity in the electrical grid
is possible in principle using state-of-the-art power-power flow models. In
practice, the detailed information needed for these physical simulations may be
unknown or prohibitively expensive to obtain. Hence, datadriven approaches to
power systems modelling, including feedforward neural networks and
auto-encoders, have been studied to leverage the increasing availability of
sensor data, but have seen limited practical adoption due to lack of
transparency and inefficiencies on large-scale problems. Our work addresses
this gap by proposing a data- and knowledge-driven probabilistic graphical
model for energy systems based on the framework of graph neural networks
(GNNs). The model can explicitly factor in domain knowledge, in the form of
grid topology or physics constraints, thus resulting in sparser architectures
and much smaller parameters dimensionality when compared with traditional
machine-learning models with similar accuracy. Results obtained from a
real-world smart-grid demonstration project show how the GNN was used to inform
grid congestion predictions and market bidding services for a distribution
system operator participating in an energy flexibility market.
