Topology Estimation Using Graphical Models in Multi-Phase Power Distribution Grids

Power distribution grids are structurally operated radially, such that energized lines form a collection of trees with a substation at the root of each tree. The operational topology 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 the radial operational structure of the distribution grid from synchronized voltage measurements. 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, and in particular Gaussian, for injections. We validate the algorithm through extensive experiments on ac three-phase IEEE distribution grid test cases.