Stealthy attack detection using convex optimization-based RPCA algorithm

Abstract

State estimation in the electric power system is the process that describes the condition of the grid by estimating the state variables using the data obtained by sensors placed in numerous parts of the grid. The continuous operation of the grid requires the state estimation to be done using the right data. To detect the existence of any bad data that may mislead state estimation, the renowned Bad Data Detection Test (BDD) is used. However, the False Data Injection Attack (FDIA) bypasses the BDD test effortlessly. Several kinds of research have been conducted to detect the presence of FDIA. This paper presents two Convex Optimization-based Robust Principal Component Analysis (RPCA) algorithms that use l1 norm as convex surrogate replacing the non-convex lo norm, for solving this problem. The first technique uses a proximal gradient algorithm that is directly applied to the primal problem. The second technique uses a gradient algorithm applied to the conjugate transpose problem. The true measurement matrix is considered as a low-rank matrix and the attack matrix as sparse and the entire problem of detecting the FDIA as a matrix recovery problem. Both these algorithms are faster several orders of magnitude than the previous advanced algorithm for this problem. The proposed detectors are tested under two attack scenarios: the random attack and the targeted attack case. The test was conducted on IEEE 30 and IEEE 118 bus test systems. Numerical results show that the proposed detectors have a better detection probability and very low average time delay of detection when the system is under both random and targeted attacks.