  Power system functionality is determined on the basis of the power system
state estimation (PSSE). Thus, corruption of the PSSE may lead to severe
consequences, such as financial losses, maintenance damage, and disruptions in
electricity distribution. Classical bad data detection (BDD) methods, developed
to ensure PSSE reliability, are unable to detect well-designed attacks, named
unobservable false data injection (FDI) attacks. In this paper, we develop
novel structural-constrained methods for the detection of unobservable FDI
attacks, the identification of the attacked buses' locations, and PSSE under
the presence of such attacks. The proposed methods are based on formulating
structural, sparse constraints on both the attack and the system loads. First,
we exploit these constraints in order to compose an appropriate model selection
problem. Then, we develop the associated generalized information criterion
(GIC) for this problem. However, for large networks, the GIC method's
computational complexity grows exponentially with the network size. Thus, based
on the proposed structural and sparse constraints, we develop two novel
low-complexity methods for unobservable FDI attack identification: 1) a
modification of the state-of-the-art orthogonal matching pursuit (OMP); and 2)
a method that utilizes the graph Markovian property in power systems, i.e. the
second-neighbor relationship between the power data at the system's buses. The
methods' performance is evaluated on a IEEE-30 bus test case system.
