  Traditionally power distribution networks are either not observable or only
partially observable. This complicates development and implementation of new
smart grid technologies, such as those related to demand response, outage
detection and management, and improved load-monitoring. In this two part paper,
inspired by proliferation of metering technology, we discuss estimation
problems in structurally loopy but operationally radial distribution grids from
measurements, e.g. voltage data, which are either already available or can be
made available with a relatively minor investment. In Part I, the objective is
to learn the operational layout of the grid. Part II of this paper presents
algorithms that estimate load statistics or line parameters in addition to
learning the grid structure. Further, Part II discusses the problem of
structure estimation for systems with incomplete measurement sets. Our newly
suggested algorithms apply to a wide range of realistic scenarios. The
algorithms are also computationally efficient -- polynomial in time -- which is
proven theoretically and illustrated computationally on a number of test cases.
The technique developed can be applied to detect line failures in real time as
well as to understand the scope of possible adversarial attacks on the grid.
