RESUMO
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.
RESUMO
This document contains supplemental material for the paper [2]. The notations in this document are the same as in [2]. In particular, we first present here the proof of Theorem 1 in [2]. This theorem expresses the locally most powerful unbiased (LMPU) test, which is a general method for local detection, in the presence of known nuisance parameters. Second, we present here the Matlab code of the LMPU and the generalized LMPU for the special case of detection of a small deviation in the frequency of sinusoidal signals, which arises in various signal processing applications.
