  This manuscript presents novel techniques for identifying the switch states,
phase identification, and estimation of equipment parameters in multi-phase low
voltage electrical grids, which is a major challenge in long-standing German
low voltage grids that lack observability and are heavily impacted by modelling
errors. The proposed methods are tailored for systems with a limited number of
spatially distributed measuring devices, which measure voltage magnitudes at
specific nodes and some line current magnitudes. The overall approach employs a
problem decomposition strategy to divide the problem into smaller subproblems,
which are addressed independently. The techniques for identifying switch states
and system phases are based on heuristics and a binary optimization problem
using correlation analysis of the measured time series. The estimation of
equipment parameters is achieved through a data-driven regression approach and
by an optimization problem, and the identification of cable types is solved
using a Mixed-Integer Quadratic Programming solver. To validate the presented
methods, a realistic grid is used and the presented techniques are evaluated
for their resilience to data quality and time resolution, discussing the
limitations of the proposed methods.
