  As electric grids experience high penetration levels of renewable generation,
fundamental changes are required to address real-time situational awareness.
This paper uses unique traits of tensors to devise a model-free situational
awareness and energy forecasting framework for distribution networks. This work
formulates the state of the network at multiple time instants as a three-way
tensor; hence, recovering full state information of the network is tantamount
to estimating all the values of the tensor. Given measurements received from
$\mu$phasor measurement units and/or smart meters, the recovery of unobserved
quantities is carried out using the low-rank canonical polyadic decomposition
of the state tensor---that is, the state estimation task is posed as a tensor
imputation problem utilizing observed patterns in measured quantities. Two
structured sampling schemes are considered: slab sampling and fiber sampling.
For both schemes, we present sufficient conditions on the number of sampled
slabs and fibers that guarantee identifiability of the factors of the state
tensor. Numerical results demonstrate the ability of the proposed framework to
achieve high estimation accuracy in multiple sampling scenarios.
