State Estimation in Power Systems Under Random Data Attack Using Correlation Matching, Semidefinite Relaxation, and Truncated Eigenvalue Decomposition

Abstract

This work considers a state estimation problem in modern power systems from the perspective of smart grids. Due to the use of digital technology, smart grids often encounter malicious data that is deliberately injected to attack their grid operations. Such kind of perturbation could be targeted at any domain of a smart grid from household customers to bulk generation, leading to network failures and power disruption. To monitor the operational health of the smart grids, power system state estimation is a crucial task and becomes challenging when a false data injection occurs. In this work, three computation methods are proposed for estimating the state vector from contaminated measurement results that are typically available in the power transmission domain of a smart grid. This work is the first that proposes the correlation matching criterion to the power state estimation. As a non-convex function, the correlation matching loss is convexified using semidefinite relaxation. Furthermore, to preserve the rank-one condition inherent in the outer product of the power state vector, the best rank-one approximation based on the eigenvalue decomposition is employed. Numerical simulation is conducted to demonstrate the usability of the proposed algorithms and to illustrate their performance. Signal-plus-attack-to-noise ratio (SANR) and phase-to-attack ratio are examples of the situational quality that can exist in the power transmission systems. Both are chosen herein as the investigational aspects for comparing the performance of the proposed methods and corresponding low-rank approaches. Numerical results reveal that for a high region of the SANR, the new methods can provide significantly less root-mean-squared error and normalized bias norm than the previous approaches. Regarding the complexity, our proposed techniques consume more computational time than two former works due to iterative computation style, yet lower than a previous sophisticated work.

Keywords

• Power system state estimation
• injection attacks
• convex optimization
• correlation matrix
• semidefinite relaxation
• eigenvalue decomposition