  The knowledge of distribution grid models, including topologies and line
impedances, is essential to grid monitoring, control and protection. However,
this information is often unavailable, incomplete or outdated. The increasing
deployment of smart meters (SMs) provides a unique opportunity to address this
issue. This paper proposes a two-stage data-driven framework for distribution
grid modeling using SM data. In the first stage, we propose to identify the
topology via reconstructing a weighted Laplacian matrix of distribution
networks, which is mathematically proven to be robust against moderately
heterogeneous R/X profiles. In the second stage, we develop nonlinear least
absolute deviations (LAD) and least squares (LS) regression models to estimate
line impedances of single branches based on a nonlinear inverse power flow,
which is then embedded within a bottom-up sweep algorithm to achieve the
identification across the network in a branch-wise manner. Because the
estimation models are inherently non-convex programs and NP-hard, we specially
address their tractable convex relaxations and verify the exactness. In
addition, we design a conductor library to significantly narrow down the
solution space. Numerical results on the modified IEEE 13-bus, 37-bus and
69-bus test feeders validate the effectiveness of the proposed methods.
