  The increasing penetration of intermittent distributed energy resources in
power networks calls for novel planning and control methodologies which hinge
on detailed knowledge of the grid. However, reliable information concerning the
system topology and parameters may be missing or outdated for temporally
varying electric distribution networks. This paper proposes an online learning
procedure to estimate the network admittance matrix capturing topological
information and line parameters. We start off by providing a recursive
identification algorithm exploiting phasor measurements of voltages and
currents. With the goal of accelerating convergence, we subsequently complement
our base algorithm with a design-of-experiment procedure which maximizes the
information content of data at each step by computing optimal voltage
excitations. Our approach improves on existing techniques, and its
effectiveness is substantiated by numerical studies on realistic testbeds.
