State Estimation in Power Systems Under False Data Injection Attack Using Total Least Squares

This work considers a state estimation problem in modern power systems, e.g., smart grids. Due to the use of digital technology, the smart grids often encounter malicious data that is deliberately injected to attack their network operations. This kind of perturbation affects the electricity stability to household users and eventually can lead to smart grid network failures. To monitor the operational health of the smart grids, the power system state estimation is a crucial task and becomes challenging when a false data injection occurs. In this work, two non-iterative computation methods based on total least squares are proposed for estimating the state vector from the measurement results contaminated by the additive noise and the malicious attack that can arise in the power transmission systems. To demonstrate the usability of the proposed algorithms and to illustrate their performance, numerical simulation is conducted taking into account two IEEE power system standards, such as IEEE 9-bus and 14-bus models. Signal-to-noise ratio (SNR), signal-and-attack-to-noise ratio (SANR), and phase-to-attack ratio are examples of the situational quality that can exist in the power distribution systems. These ratios are considered as the investigational aspects for comparing the performance of the proposed methods and corresponding low-rank approaches. Numerical results reveal that our proposed techniques consume much less computational time than two former works for all ranges of the SNR and the SANR. Regarding the estimation accuracy, for moderate and high regions of the SNR and the SANR, the two new methods provide significantly less root-mean-squared error and normalized bias norm than the two previous approaches. For the problem size solvability point of view, the traditional low-rank methods suffer from the trivial solution caused by too many unknown convex optimization variables due to a large number of time samples, whereas the proposed TLS-based algorithms can handle a large power distribution system with a large number of time samples.