Impact of stealthy false data injection attacks on power flow of power transmission lines—A mathematical verification

• DC power flow analysis. • Matrix analysis and graph theory. • Determination of the impacts of having full and partial knowledge of true values of the system information in stealthy false data injection attacks on power flow changes of power transmission lines. • Determination of the maximum possible power flow changes of power transmission lines in case of stealthy false data injection attacks on the target power transmission line. • Vulnerability assessment. Stealthy False Data Injection (SFDI) attacks in power systems can lead to a large-scale cascading failure, if not detected and eliminated quickly. The impact of such attacks can be minimized by using advanced control and protection mechanisms. This paper aims to provide mathematical proof for validation of the impact of SFDI attacks on power flow changes of power transmission lines equipped with metering devices based on graph theory, regardless of the network topology. In particular, it is assumed that an adversary attack targets a set of power transmission lines that are highly vulnerable to SFDI attacks, and corrupts the measurements, thus, changing the power flow of the entire power transmission system, leading to wrong power dispatches. Subsequently, an index is defined to show the power flow changes in case of SFDI attacks considering full and partial knowledge of true values of the system information. In addition, the valid boundaries of possible values for the defined index are determined. The proposed theorem can show how a controller can take protective measures to enhance the safety and reliability of power systems.