The problem of malicious false data injection in power grid state estimators has recently gained considerable attention. Most of this attention, however, has been focused on the assumption of a centralised state estimator. In a next-generation smart grid environment incorporating distributed generation and highly variable demand induced by electric mobility, distributed state estimation is highly desirable to enhance overall grid robustness. We therefore consider the case of a bi-level hierarchical state estimator, which provides only partial observability to lower-tier state estimators.

Using a formal observability model, we consider the case of an active adversary able to modify a set of measurements and derive bounds on the maximum number of manipulated measurements that can be tolerated, the composition of attack vectors, and give a formulation for identifying minimal sets of additional measurements to tolerate k-measurement attacks in this hierarchical state estimator. This allows us a more rigorous formulation over existing models.