  Distribution grid is the medium and low voltage part of a large power system.
Structurally, the majority of distribution networks operate radially, such that
energized lines form a collection of trees, i.e. forest, with a substation
being at the root of any tree. The operational topology/forest may change from
time to time, however tracking these changes, even though important for the
distribution grid operation and control, is hindered by limited real-time
monitoring. This paper develops a learning framework to reconstruct radial
operational structure of the distribution grid from synchronized voltage
measurements in the grid subject to the exogenous fluctuations in nodal power
consumption. To detect operational lines our learning algorithm uses
conditional independence tests for continuous random variables that is
applicable to a wide class of probability distributions of the nodal
consumption and Gaussian injections in particular. Moreover, our algorithm
applies to the practical case of unbalanced three-phase power flow. Algorithm
performance is validated on AC power flow simulations over IEEE distribution
grid test cases.
