  Widely available measurement equipment in electrical distribution grids, such
as power-quality measurement devices, substation meters, or customer smart
meters do not provide phasor measurements due to the lack of high resolution
time synchronisation. Instead such measurement devices allow to obtain
magnitudes of voltages and currents and the local phase angle between those. In
addition, these measurements are subject to measurement errors of up to few
percent of the measurand. In order to utilize such measurements for grid
monitoring, this paper presents and assesses a stochastic grid calculation
approach that allows to derive confidence regions for the resulting current and
voltage phasors. Two different metering models are introduced: a PMU model,
which is used to validate theoretical properties of the estimator, and an
Electric Meter model for which a Gaussian approximation is introduced. The
estimator results are compared for the two meter models and case study results
for a real Danish distribution grid are presented.
