  This paper proposes a model-free distribution system state estimation method
based on tensor completion using canonical polyadic decomposition. In
particular, we consider a setting where the network is divided into multiple
areas. The measured physical quantities at buses located in the same area are
processed by an area controller. A three-way tensor is constructed to collect
these measured quantities. The measurements are analyzed locally to recover the
full state information of the network. A distributed closed-form iterative
algorithm based on the alternating direction method of multipliers is developed
to obtain the low-rank factors of the whole network state tensor where
information exchange happens only between neighboring areas. The convergence
properties of the distributed algorithm and the sufficient conditions on the
number of samples for each smaller network that guarantee the identifiability
of the factors of the state tensor are presented. To demonstrate the efficacy
of the proposed algorithm and to check the identifiability conditions,
numerical simulations are carried out using the IEEE 123-bus system.
