Data-Driven and Online Estimation of Linear Sensitivity Distribution Factors: A Low-rank Approach

TL;DR

This paper introduces a robust, low-rank, online method for estimating sensitivity matrices in electrical grids, capable of handling missing data and outliers, with proven convergence and effectiveness.

Contribution

It presents a novel online proximal-gradient approach for real-time sensitivity estimation that outperforms least-squares methods, especially with limited or imperfect data.

Findings

Effective estimation with fewer measurements

Robustness to missing data and outliers

Convergence in terms of dynamic regret

Abstract

Estimation of sensitivity matrices in electrical transmission systems allows grid operators to evaluate in real-time how changes in power injections reflect into changes in power flows. In this paper, we propose a robust low-rank minimization approach to estimate sensitivity matrices based on measurements of power injections and power flows. An online proximal-gradient method is proposed to estimate sensitivities on-the-fly from real-time measurements. The proposed method obtains meaningful estimates with fewer measurements when the regression model is underdetermined, in contrast with existing methods based on least-squares approaches. In addition, our method can also identify faulty measurements and handle missing data. In this work, convergence results in terms of dynamic regret are presented. Numerical tests corroborate the effectiveness of the novel approach and the robustness of missing measurements and outliers.