  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. 
Knowledge- and Data-driven Services for Energy Systems using Graph   Neural Networks