  Limited presence of nodal and line meters in distribution grids hinders their
optimal operation and participation in real-time markets. In particular lack of
real-time information on the grid topology and infrequently calibrated line
parameters (impedances) adversely affect the accuracy of any operational power
flow control. This paper suggests a novel algorithm for learning the topology
of distribution grid and estimating impedances of the operational lines with
minimal observational requirements - it provably reconstructs topology and
impedances using voltage and injection measured only at the terminal (end-user)
nodes of the distribution grid. All other (intermediate) nodes in the network
may be unobserved/hidden. Furthermore no additional input (e.g., number of grid
nodes, historical information on injections at hidden nodes) is needed for the
learning to succeed. Performance of the algorithm is illustrated in numerical
experiments on the IEEE and custom power distribution models.
