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With the rising penetration of distributed energy resources, distribution system control and enabling techniques such as state estimation have become essential to distribution system operation. However, traditional state estimation techniques have difficulty coping with the low-observability conditions often present on the distribution system due to the paucity of sensors and heterogeneity of measurements. To address these limitations, we propose a distribution system state estimation algorithm that employs matrix completion (a tool for estimating missing values in low-rank matrices) augmented with noise-resilient power flow constraints. This method operates under low-observability conditions where standard least-squares-based methods cannot operate, and flexibly incorporates any network quantities measured in the field. We empirically evaluate our method on the IEEE 33- and 123-bus test systems, and find that it provides near-perfect state estimation performance (within 1% mean absolute percent error) across many low-observability data availability regimes.
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of c
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 const
The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the optimization pro
We exploit the versatile framework of Riemannian optimization on quotient manifolds to develop R3MC, a nonlinear conjugate-gradient method for low-rank matrix completion. The underlying search space of fixed-rank matrices is endowed with a novel Riem
We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the particular least