Estimation of Sensitivities: Low-rank Approach and Online Algorithms for Streaming Measurements

Abstract

This paper focuses on the estimation of sensitivity matrices in power grids, with applications in both transmission and distribution systems. By leveraging a low-rank approximation of certain classes of sensitivity matrices, the paper proposes a robust nuclear norm minimization method to estimate sensitivities from measurements. Relative to existing methods based on the least-squares approach, the proposed method can obtain meaningful estimates with a smaller number of measurements and when the regression model is underdetermined; the method can also identify faulty measurements and handle missing data. Furthermore, an online proximal-gradient method is proposed to estimate sensitivities on-the-fly from real-time measurements; convergence results in terms of dynamic regret are offered in this case. Tests corroborate the effectiveness of the novel approach.Comment: Submitted to IEEE Transactions on Smart Gri