  The advanced operation of future electricity distribution systems is likely
to require significant observability of the different parameters of interest
(e.g., demand, voltages, currents, etc.). Ensuring completeness of data is,
therefore, paramount. In this context, an algorithm for recovering missing
state variable observations in electricity distribution systems is presented.
The proposed method exploits the low rank structure of the state variables via
a matrix completion approach while incorporating prior knowledge in the form of
second order statistics. Specifically, the recovery method combines nuclear
norm minimization with Bayesian estimation. The performance of the new
algorithm is compared to the information-theoretic limits and tested trough
simulations using real data of an urban low voltage distribution system. The
impact of the prior knowledge is analyzed when a mismatched covariance is used
and for a Markovian sampling that introduces structure in the observation
pattern. Numerical results demonstrate that the proposed algorithm is robust
and outperforms existing state of the art algorithms.
