  This paper defines a Maximum Likelihood Estimator (MLE) for the admittance
matrix estimation of distribution grids, utilising voltage magnitude and power
measurements collected only from common, unsychronised measuring devices (Smart
Meters). First, we present a model of the grid, as well as the existing MLE
based on voltage and current phasor measurements. Then, this problem
formulation is adjusted for phase-less measurements using common assumptions.
The effect of these assumptions is compared to the initial problem in various
scenarios. Finally, numerical experiments on a popular IEEE benchmark network
indicate promising results. Missing data can greatly disrupt estimation
methods. Not measuring the voltage phase only adds 30\% of error to the
admittance matrix estimate in realistic conditions. Moreover, the sensitivity
to measurement noise is similar with and without the phase.
