Designing Sparse AC False Data Injection Attack

False Data Injection (FDI) attacks pose significant threats by manipulating measurement data, leading to incorrect state estimation. Although numerous studies have focused on designing DC FDI attacks, few have addressed AC FDI attacks due to the complexity of incorporating non-linear AC power flows in the design process. Additionally, designing a sparse AC FDI attack presents another challenge because it involves solving a mixed-integer nonlinear programming problem with nonconvex constraints, which is inherently difficult. This paper explores the design and implementation of a sparse AC FDI attack, where the attacker strategically selects a minimal set of measurements to manipulate while maintaining the nonlinearity and interdependence of AC power flow equations. The objective is to minimize the number of altered measurements, thereby reducing the attack's detectability while achieving the desired state estimation error. The problem is formulated as a Mixed Integer Nonlinear Programming (MINLP) problem. Binary variables indicate the selection of measurements to be manipulated, and continuous variables represent the measurement values. An optimization problem is designed to minimize the number of binary variables, translating into a sparse attack, while ensuring the attack remains efficient and hard to detect. The big-M method and conditional constraints are utilized to handle the fixed and variable measurement parameters effectively. Simulation results on the standard IEEE 57-bus test system demonstrate the efficacy of the sparse AC FDI attack in terms of its impact on state estimation and the minimal number of measurements required for successful implementation.