Model-Free State Estimation Using Low-Rank Canonical Polyadic Decomposition
This addresses the need for improved situational awareness in distribution networks, but it is incremental as it applies tensor decomposition methods to a specific domain.
The paper tackles the problem of real-time state estimation in electric grids with high renewable generation by formulating network states as a three-way tensor and recovering unobserved quantities using low-rank canonical polyadic decomposition, achieving high estimation accuracy in various sampling scenarios.
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 $μ$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.