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Efficient operation of distribution grids in the smart-grid era is hinderedby the limited presence of real-time nodal and line meters. In particular, thisprevents the easy estimation of grid topology and associated line parametersthat are necessary for control and optimization efforts in the grid. This paperstudies the problems of topology and parameter estimation in radial balanceddistribution grids where measurements are restricted to only the leaf nodes andall intermediate nodes are unobserved/hidden. To this end, we propose two exactlearning algorithms that use balanced voltage and injection measured only atthe end-users. The first algorithm requires time-stamped voltage samples,statistics of nodal power injections and permissible line impedances to recoverthe true topology. The second and improved algorithm requires only time-stampedvoltage and complex power samples to recover both the true topology andimpedances without any additional input (e.g., number of grid nodes, statisticsof injections at hidden nodes, permissible line impedances). We prove thecorrectness of both learning algorithms for grids where unobserved buses/nodeshave a degree greater than three and discuss extensions to regimes where thatassumption doesn't hold. Further, we present computational and, moreimportantly, the sample complexity of our proposed algorithm for joint topologyand impedance estimation. We illustrate the performance of the designedalgorithms through numerical experiments on the IEEE and custom powerdistribution models.

Learning with End-Users in Distribution Grids: Topology and Parameter Estimation