Robust Recovery of Missing Data in Electricity Distribution Systems

TL;DR

This paper introduces a robust matrix completion algorithm that combines nuclear norm minimization with Bayesian estimation to recover missing data in electricity distribution systems, enhancing observability and data completeness.

Contribution

It presents a novel algorithm that leverages low rank structure and prior statistical knowledge for improved missing data recovery in power systems.

Findings

Outperforms existing algorithms in accuracy and robustness.

Effective even with mismatched prior covariance.

Validated on real urban low voltage distribution data.

Abstract

The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore, paramount. In this context, an algorithm for recovering missing state variable observations in electricity distribution systems is presented. The proposed method exploits the low rank structure of the state variables via a matrix completion approach while incorporating prior knowledge in the form of second order statistics. Specifically, the recovery method combines nuclear norm minimization with Bayesian estimation. The performance of the new algorithm is compared to the information-theoretic limits and tested trough simulations using real data of an urban low voltage distribution system. The impact of the prior knowledge is analyzed when a mismatched covariance is used and for a Markovian sampling that introduces structure in the observation pattern. Numerical results demonstrate that the proposed algorithm is robust and outperforms existing state of the art algorithms.