Structure Learning and Statistical Estimation in Distribution Networks - Part I

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.