  The increasing penetration of distributed energy resources poses numerous
reliability issues to the urban distribution grid. The topology estimation is a
critical step to ensure the robustness of distribution grid operation. However,
the bus connectivity and grid topology estimation are usually hard in
distribution grids. For example, it is technically challenging and costly to
monitor the bus connectivity in urban grids, e.g., underground lines. It is
also inappropriate to use the radial topology assumption exclusively because
the grids of metropolitan cities and regions with dense loads could be with
many mesh structures. To resolve these drawbacks, we propose a data-driven
topology estimation method for MV and LV distribution grids by only utilizing
the historical smart meter measurements. Particularly, a probabilistic
graphical model is utilized to capture the statistical dependencies amongst bus
voltages. We prove that the bus connectivity and grid topology estimation
problems, in radial and mesh structures, can be formulated as a linear
regression with a least absolute shrinkage regularization on grouped variables
(\textit{group lasso}). Simulations show highly accurate results in eight MV
and LV distribution networks at different sizes and 22 topology configurations
using PG\&E residential smart meter data.
