Mahalanobis distance-based robust approaches against false data injection attacks on dynamic power state estimation

Abstract

State estimation plays a crucial role in the daily operation of power systems. Although many researchers have studied false data injection (FDI) attacks in power state estimation, current state estimation approaches are still highly vulnerable to FDI attacks. Currently, most existing studies on FDI attacks focus on static state estimation (SSE), where power system states are not changed with time, and one of them includes the discovery of three efficient FDI attacks that can introduce arbitrary large errors into certain state variables without being detected by existing bad measurement detection algorithms. In reality, however, power states are varied with time in real-world power systems. In this paper, we investigate the problem of the above three FDI attacks against dynamic power state estimation (DSE), where power system states are dynamically changed with time. Although the three attacks were discovered in SSE several years ago, none of them has been well addressed in static power state systems. In this research, we propose two robust defense approaches against the above three efficient FDI attacks on DSE. Compared to existing approaches, our proposed approaches have three major differences and significant strengths: (1) they defend against the three FDI attacks on dynamic power state estimation rather than static power state estimation, (2) they give a robust estimator that can accurately extract a subset of attack-free sensors for power state estimation, and (3) they adopt the little-known Mahalanobis distance in the consistency check of power sensor measurements, which is different from the Euclidean distance used in all the existing studies on power state estimation. We mathematically prove that the Mahalanobis distance is not only useful but also much better than the Euclidean distance in the consistency check of power sensor measurements. Our time complexity analysis shows that the proposed two robust defense approaches are efficient. Moreover, in order to demonstrate the effectiveness of the proposed approaches, we compare them with the three wellknown approaches: the least square approach, the Imhotep-SMT approach, and the MEE-UKF approach. Experiments show that the proposed approaches further reduce the estimation error by two orders of magnitude and four orders of magnitude compared to the Imhotep-SMT approach and the least square approach, respectively. Whereas our approach has a similar root mean square error as the Imhotep-SMT approach has, our approach provides a more stable result.