  State estimation is highly critical for accurately observing the dynamic
behavior of the power grids and minimizing risks from cyber threats. However,
existing state estimation methods encounter challenges in accurately capturing
power system dynamics, primarily because of limitations in encoding the grid
topology and sparse measurements. This paper proposes a physics-informed
graphical learning state estimation method to address these limitations by
leveraging both domain physical knowledge and a graph neural network (GNN). We
employ a GNN architecture that can handle the graph-structured data of power
systems more effectively than traditional data-driven methods. The
physics-based knowledge is constructed from the branch current formulation,
making the approach adaptable to both transmission and distribution systems.
The validation results of three IEEE test systems show that the proposed method
can achieve lower mean square error more than 20% than the conventional
methods.
