Cross-variance analysis to online estimate power flow Jacobian matrix using limited PMU data

Abstract

This paper proposes a data-driven approach to estimate the power flow Jacobian matrix online with only small-scale data set collected by phasor measurement unit (PMU). For data in limited amount, one of the greatest challenges to estimate the Jacobian matrix is how to quantify and treat the interference of multiple uncertainties, which are analytically intractable by traditional approaches. To tackle these uncertainties, in this work, through analyzing the cross-variance matrix between voltage measurements and load data, the joint density probability of uncertainties is modeled in matrix-level. Furthermore, a random matrix theory (RMT) based approach is proposed to shrink the singular values of the cross-variance matrix to alleviate the unfavorable influence of uncertainties. This approach is based on the property that the singular values of a random matrix are asymptotically converged to a deterministic distribution. Numerous cases prove that the proposed method is capable of obtaining more precise estimation results even with limited PMU data. Besides, this estimation would supply extra information assistant for power system monitoring, such as voltage stability assessment (VSA) and topology change detection (TCD).