State Estimation in Partially Observable Power Systems via Graph Signal Processing Tools

Abstract

This paper considers the problem of estimating the states in an unobservable power system, where the number of measurements is not sufficiently large for conventional state estimation. Existing methods are either based on pseudo-data that is inaccurate or depends on a large amount of data that is unavailable in current systems. This study proposes novel graph signal processing (GSP) methods to overcome the lack of information. To this end, first, the graph smoothness property of the states (i.e., voltages) is validated through empirical and theoretical analysis. Then, the regularized GSP weighted least squares (GSP-WLS) state estimator is developed by utilizing the state smoothness. In addition, a sensor placement strategy that aims to optimize the estimation performance of the GSP-WLS estimator is proposed. Simulation results on the IEEE 118-bus system show that the GSP methods reduce the estimation error magnitude by up to two orders of magnitude compared to existing methods, using only 70 sampled buses, and increase of up to 30% in the probability of bad data detection for the same probability of false alarms in unobservable systems The results conclude that the proposed methods enable an accurate state estimation, even when the system is unobservable, and significantly reduce the required measurement sensors.

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

“…• GTV-GHPF: Based on our results in [50], [62], an alert to an attack is provided if the GSP-based detector in (16) when using the GTV-GHPF in (10) (11) in (16). In addition, we verified that the BDD detector cannot detect any of the unobservable FDI attacks.…”

“…The GSP-based detector in ( 16) is based on the assumption that the state vector, θ, is a smooth graph signal w.r.t. to L = B, i.e., that T V G (θ) = θ T Lθ is small compared to other signals in the system, as shown in [40], [62]. In contrast, the state attack vector, c, is a general arbitrary vector that is not smooth w.r.t.…”

Estimation of the Admittance Matrix in Power Systems Under Laplacian and Physical Constraints

“…Using the fact that the off-diagonal entries in the matrices G and B are non-positive (Constraint C.3), we can further simplify the expression in (8) by neglecting the absolute-value operator (see Equation (10) in [60]). That is, we note that…”

“…Examples include semi-supervised learning, dimensionality reduction, community detection in complex networks, spectral clustering, and solving partial differential equations on graphs. It can also be used to define notions of smoothness and regularity on graphs, making it a powerful tool for analyzing and understanding the structure of complex data [2]- [4]. Thus, the estimation of the Laplacian matrix is a fundamental task in various fields.…”

“…Complex-valued graph signals arise in several real-world applications [5], such as multi-agent systems [6], wireless communication systems [7], voltage and power phasors in electrical networks [8]- [10], and probabilistic graphical models with complex-valued multivariate Gaussian vectors [11]. Despite the widespread use of complex-valued graph signals, the recovery of complex-valued Laplacians is a crucial problem that has not been well explored.…”