  Many researchers have studied false data injection (FDI) attacks in power
state estimation, but existing state estimation approaches are still highly
vulnerable to FDI attacks. In this paper, we investigate the problem of the
above three FDI attacks against dynamic power state estimation (DSE). 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 two proposed robust defense approaches are
efficient. Moreover, in order to demonstrate the effectiveness of the proposed
approaches, we compare them with the three well-known approaches: the least
square approach, the Imhotep-SMT approach, and the MEE-UKF approach. Our
extensive 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. Moreover, our approach is more stable than the MEE-UKF approach.
