Structure learning in power distribution networks

Traditional power distribution networks suffer from a lack of real-time observability. 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 paper, inspired by proliferation of metering technology, we discuss topology estimation problems in structurally loopy but operationally radial distribution grids from measurements, for example, voltage data, which are either already available or can be made available with a relatively minor investment. The primary objective of this paper is to learn the operational layout of the grid. Further, the structure learning algorithm is extended to cases with missing data, where available observations are limited to a fraction of the grid nodes. The algorithms are computationally efficient - polynomial in time - which is proven theoretically and illustrated in numerical experiments on a number of test cases. The techniques 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.