State Estimation in Unobservable Power Systems via Graph Signal Processing Tools

Abstract

We consider the problem of estimating the states and detecting bad data in an unobservable power system. To this end, we propose novel graph signal processing (GSP) methods. The main assumption behind the proposed GSP approach is that the grid state vector, which includes the phases of the voltages in the system, is a smooth graph signal with respect to the system admittance matrix that represents the underlying graph. Thus, the first step in this paper is to validate the graph-smoothness assumption of the states, both empirically and theoretically. Then, we develop the regularized weighted least squares (WLS) state estimator, which does not require observability of the network. We propose a sensor (meter) placement strategy that aims to optimize the estimation performance of the proposed GSP-WLS estimator. In addition, we develop a joint bad-data and falsedata injected (FDI) attacks detector that integrates the GSP-WLS state estimator into the conventional J(θ)-test with an additional smoothness regularization. Numerical results on the IEEE 118bus test-case system demonstrate that the new GSP methods outperform commonly-used estimation and detection approaches in electric networks and are robust to missing data.

Structural-Constrained Methods for the Identification of False Data Injection Attacks in Power Systems

“…In this subsection, we apply the OMP algorithm for the sparse recovery of the state attack vector, c, which is a sparse signal as described in Assumption A.3, from the measurements in (17). It should be noted that the measurement model in (17) contains a nuisance parameter vector, H L,V ∆θ θ θ , which is not a part of the conventional sparse recovery model.…”

“…Hence, as shown in (12), there exists a subset of nodes, Λ i ∈ G K c , that fully contains the attack. By substituting (12) in (17) we obtain…”

“…However, these approaches require integrating additional hardware into the power system, which results in high cost, a long installation period, and additional security vulnerabilities [16]. In addition, they may result in an unobservable system [1], [17]. Detection and identification by the moving target defense technique, where the system configuration is actively changed, have been proposed in [18], [19], and [20], respectively.…”

Multi-Area Distribution System State Estimation via Distributed Tensor Completion

“…The identifiability conditions of the tensor completion using the centralized CPD model were studied by [24] and [27]; however, the identifiability conditions in these two references require all the measurements to be synchronized across the entire system, and the conditions apply only to specific uniform sampling schemes. In this section, we provide more general identifiability conditions of the tensor completion using the multi-area CPD model (4), which also covers the case of the centralized CPD model. Our identifiability conditions allow for asynchronous samplings among different areas, and they apply to any sampling scheme.…”

“…Unlike redundant measurements in transmission systems, the measured information in secondary substations of distribution systems is scarce, which poses a formidable challenge to DSSE [3]. To address the challenge, [4] developed a graph signal processing based weighted least squares method and…”