  New methods that exploit sparse structures arising in smart grid networks are
proposed for the state estimation problem when data injection attacks are
present. First, construction strategies for unobservable sparse data injection
attacks on power grids are proposed for an attacker with access to all network
information and nodes. Specifically, novel formulations for the optimization
problem that provide a flexible design of the trade-off between performance and
false alarm are proposed. In addition, the centralized case is extended to a
distributed framework for both the estimation and attack problems. Different
distributed scenarios are proposed depending on assumptions that lead to the
spreading of the resources, network nodes and players. Consequently, for each
of the presented frameworks a corresponding optimization problem is introduced
jointly with an algorithm to solve it. The validity of the presented procedures
in real settings is studied through extensive simulations in the IEEE test
systems.
