  Accurate estimates of network parameters are essential for modeling,
monitoring, and control in power distribution systems. In this paper, we
develop a physics-informed graphical learning algorithm to estimate network
parameters of three-phase power distribution systems. Our proposed algorithm
uses only readily available smart meter data to estimate the three-phase series
resistance and reactance of the primary distribution line segments. We first
develop a parametric physics-based model to replace the black-box deep neural
networks in the conventional graphical neural network (GNN). Then we derive the
gradient of the loss function with respect to the network parameters and use
stochastic gradient descent (SGD) to estimate the physical parameters. Prior
knowledge of network parameters is also considered to further improve the
accuracy of estimation. Comprehensive numerical study results show that our
proposed algorithm yields high accuracy and outperforms existing methods.
