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.