Feasibility Assessment of AC False Data Injection Attacks in Power Systems Using Quadratic Convex Relaxation

Ensuring the security of power systems against cyber-physical threats is increasingly critical as grid operations become more dependent on measurement-driven decisionmaking. Among such threats, AC False Data Injection (FDI) attacks are particularly challenging to detect and mitigate due to the nonlinearity and nonconvexity of AC power flow equations, which complicate both attack design and feasibility analysis. This paper proposes a novel approach to assess the feasibility of AC FDI attacks using a Quadratic Convex (QC) relaxation of the power flow problem. By transforming the original nonconvex attack design formulation into a convex optimization problem, the proposed method provides a rigorous and computationally efficient tool to determine whether a stealthy AC FDI attack is physically realizable. If the relaxed problem is infeasible, it guarantees that no attack exists under the given constraints, independent of local solver limitations. The framework is implemented and evaluated on both the IEEE 39- and IEEE 118- bus test systems to examine a wide range of network conditions, attack zones, and overload targets. Simulation results demonstrate that QC relaxation enables clear identification of feasible and infeasible attack regions, and provides critical insight into how system topology and constraint settings impact vulnerability. This method enhances grid security and supports resilient grid operation by offering a formal mechanism to screen for viable attack strategies before deployment or real-time monitoring.