  This paper considers the low-observability state estimation problem in power
distribution networks and develops a decentralized state estimation algorithm
leveraging the matrix completion methodology. Matrix completion has been shown
to be an effective technique in state estimation that exploits the low
dimensionality of the power system measurements to recover missing information.
This technique can utilize an approximate (linear) load flow model, or it can
be used with no physical models in a network where no information about the
topology or line admittance is available.
  The direct application of matrix completion algorithms requires solving a
semi-definite programming (SDP) problem, which becomes infeasible for large
networks. We therefore develop a decentralized algorithm that capitalizes on
the popular proximal alternating direction method of multipliers (proximal
ADMM). The method allows us to distribute the computation among different areas
of the network, thus leading to a scalable algorithm. By doing all computations
at individual control areas and only communicating with neighboring areas, the
algorithm eliminates the need for data to be sent to a central processing unit
and thus increases efficiency and contributes to the goal of autonomous control
of distribution networks. We illustrate the advantages of the proposed
algorithm numerically using standard IEEE test cases.
