  This paper examines the problem of state estimation in power distribution
systems under low-observability conditions. The recently proposed constrained
matrix completion method which combines the standard matrix completion method
and power flow constraints has been shown to be effective in estimating voltage
phasors under low-observability conditions using single-snapshot information.
However, the method requires solving a semidefinite programming (SDP) problem,
which becomes computationally infeasible for large systems and if
multiple-snapshot (time-series) information is used. This paper proposes an
efficient algorithm to solve the constrained matrix completion problem with
time-series data. This algorithm is based on reformulating the matrix
completion problem as a bilinear (non-convex) optimization problem, and
applying the alternating minimization algorithm to solve this problem. This
paper proves the summable convergence of the proposed algorithm, and
demonstrates its efficacy and scalability via IEEE 123-bus system and a real
utility feeder system. This paper also explores the value of adding more data
from the history in terms of computation time and estimation accuracy.
