  The growing complexity of the power grid, driven by increasing share of
distributed energy resources and by massive deployment of intelligent
internet-connected devices, requires new modelling tools for planning and
operation. Physics-based state estimation models currently used for data
filtering, prediction and anomaly detection are hard to maintain and adapt to
the ever-changing complex dynamics of the power system. A data-driven approach
based on probabilistic graphs is proposed, where custom non-linear, localised
models of the joint density of subset of system variables can be combined to
model arbitrarily large and complex systems. The graphical model allows to
naturally embed domain knowledge in the form of variables dependency structure
or local quantitative relationships. A specific instance where neural-network
models are used to represent the local joint densities is proposed, although
the methodology generalises to other model classes. Accuracy and scalability
are evaluated on a large-scale data set representative of the European
transmission grid.
