Protection strategies against false data injection attacks with uncertain information on electric power grids

False data injection attacks have recently been introduced as one of important issues related to cyber-attacks on electric power grids. These attacks aim to compromise the readings of multiple power meters in order to mislead the operation and control centers. Recent studies have shown that if a malicious attacker has complete knowledge of the power grid topology and branch admittances, s/he can adjust the false data injection attack such that the attack remains undetected and successfully passes the bad data detection tests that are used in power system state estimation. In this paper, we investigate that a practical false data injection attack is essentially a cyber-attack with uncertain information due to the attackers lack of knowledge with respect to the power grid parameters because the attacker has limited physical access to electric facilities and limited resources to compromise meters. We mathematically formulated a method of identifying the most vulnerable locations to false data injection attack. Furthermore, we suggest minimum topology changes or phasor measurement units (PMUs) installation in the given power grids for mitigating such attacks and indicate a new security metrics that can compare different power grid topologies. The proposed metrics for performance is verified in standard IEEE 30-bus system. We show that the robustness of grids can be improved dramatically with minimum topology changes and low cost.