Leveraging Convex Relaxation to Identify the Feasibility of Conducting AC False Data Injection Attack in Power Systems

TL;DR

This work addresses the feasibility assessment of AC FDI attacks in power systems, where nonlinear AC power-flow equations hinder straightforward feasibility checks. It proposes solving a convexified AC FDI design using a Quadratic Convex ($QC$) relaxation to obtain a convex quadratic program, with the central claim that if the convexified problem is infeasible, then the original nonconvex design is infeasible regardless of solver performance. The method is demonstrated on the IEEE 118-bus test system to explore how attack-zone selection and constraints (e.g., the overload bound $W$) affect feasibility. The approach provides a practical tool for security analysis and lays a foundation for future work on sparse AC FDI attacks and defenses.

Abstract

FDI (False Data Injection) attacks are critical to address as they can compromise the integrity and reliability of data in cyber-physical systems, leading to potentially severe consequences in sectors such as power systems. The feasibility of FDI attacks has been extensively studied from various perspectives, including access to measurements and sensors, knowledge of the system, and design considerations using residual-based detection methods. Most research has focused on DC-based FDI attacks; however, designing AC FDI attacks involves solving a nonlinear optimization problem, presenting additional challenges in assessing their feasibility. Specifically, it is often unclear whether the infeasibility of some designed AC FDI attacks is due to the nonconvexity and nonlinearity inherent to AC power flows or if it stems from inherent infeasibility in specific cases, with local solvers returning infeasibility. This paper addresses this issue by leveraging the principle that if a convexified AC FDI attack design problem is infeasible, the attack design itself is infeasible, irrespective of nonlinear solution challenges. We propose an AC FDI attack design based on convexified power flow equations and assess the feasibility of the proposed attack by examining the extent of the attackable region. This approach utilizes a Quadratic Convex (QC) relaxation technique to convexify AC power flows. To evaluate the proposed method, we implement it on the IEEE 118-bus test system and assess the feasibility of an AC FDI attack across various attack zones.

Figures (2)

• Figure 1: One-line diagram depicting the IEEE 118-bus test system, with the attack zones indicated.
• Figure 2: Third attack zone in One-line diagram of the IEEE 118-bus test system.