  Implementing state estimation in low and medium voltage power distribution is
still challenging given the scale of many networks and the reliance of
traditional methods on a large number of measurements. This paper proposes a
method to improve voltage predictions in real-time by leveraging a limited set
of real-time measurements. The method relies on Bayesian estimation formulated
as a linear least squares estimation problem, which resembles the classical
weighted least-squares (WLS) approach for scenarios where full network
observability is not available. We build on recently developed linear
approximations for unbalanced three-phase power flow to construct voltage
predictions as a linear mapping of load predictions constructed with Gaussian
processes. The estimation step to update the voltage forecasts in real-time is
a linear computation allowing fast high-resolution state estimate updates. The
uncertainty in forecasts can be determined a priori and smoothed a posteriori,
making the method useful for both planning, operation and post-hoc analysis.
The method outperforms conventional WLS and is applied to different test
feeders and validated on a real test feeder with the utility Alliander in The
Netherlands.
