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

Efficient operation of distribution grids in the smartgrid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents easy estimation of grid topology and associated line parameters that are necessary for control and optimization efforts in the grid. This paper studies the problems of topology and parameter estimation in the limited observability regime where measurements are restricted to only the terminal nodes of the grid and all intermediate nodes are unobserved/hidden. To this end, we propose two algorithms for exact topology (and impedances) estimation that provably reconstruct topology using voltage and injection measured only at the end-users of the distribution grid. The first algorithm requires time stamped voltage samples, statistics of nodal power injections and permissible line impedances to recover the true topology. The second and improved algorithm requires only timestamped voltage/complex power samples to recover both the true topology and impedances without any additional input (e.g., number of grid nodes, statistics of injections at hidden nodes, permissible line impedances). We discuss the computational and sample complexity of our proposed algorithms and demonstrate that topology (and impedance) estimation by our algorithms are optimal with respect to number of nodal observability required. We illustrate their performance through numerical experiments on the IEEE and custom power distribution models.