Power Systems Topology and State Estimation by Graph Blind Source Separation

Abstract

In this paper, we consider the problem of blind estimation of states and topology (BEST) in power systems. We use the linearized DC model of real power measurements with unknown voltage phases (i.e. states) and an unknown admittance matrix (i.e. topology) and show that the BEST problem can be formulated as a blind source separation (BSS) problem with a weighted Laplacian mixing matrix. We develop the constrained maximum likelihood (ML) estimator of the Laplacian matrix for this graph BSS (GBSS) problem with Gaussian-distributed states. The ML-BEST is shown to be only a function of the states' second-order statistics. Since the topology recovery stage of the ML-BEST approach results in a high-complexity optimization problem, we propose two low-complexity methods to implement it: (1) Two-phase topology recovery, which is based on solving the relaxed convex optimization and then finding the closest Laplacian matrix, and (2) Augmented Lagrangian topology recovery. We derive a closed-form expression for the associated Cramér-Rao bound (CRB) on the topology matrix estimation. The performance of the proposed methods is evaluated for the IEEE-14 bus test-case system and for a random network. It is shown that, asymptotically, the state estimation performance of the proposed ML-BEST methods coincides with the oracles minimum mean-squared-error (MSE) state estimator, and the MSE of the topology estimation achieves the proposed CRB.

Detection of False Data Injection Attacks in Smart Grids Based on Graph Signal Processing

“…The averaged threshold from (25) is statistically more robust to outliers than the maximum threshold from (24). Consistently, our simulations showed that, indeed, the threshold value from (25) led to better results than the one from (24).…”

Robust Adaptive Estimation of Graph Signals Based on Welsch Loss

“…It is because that graph signal recovery and estimate have been widely studied with many promising applications. Applications contain power systems estimation [55][56][57][58], network time synchronization, and data registration [59,60].…”

Multisource Fault Signal Separation of Rotating Machinery Based on Wavelet Packet and Fast Independent Component Analysis

“…In blind signal separation, the typical algorithms commonly used include the fast fixed-point algorithm [37], natural gradient algorithm [38], Equivariant Adaptive Separation via Independence (EASI) algorithm [39,40], and Joint Approximation Diagonalization of Eigen-matrices (JADE) algorithm [41,42], etc. Grotas et al [43] developed the constrained maximum likelihood (ML) estimator of the Laplacian matrix for this graph BSS problem with Gaussian-distributed states. Eitner et al [44] used two blind source separation algorithms to estimate the modal parameters of a reduced-scale rocket nozzle using only measurements of deformation.…”