[Paper Review] Vulnerability Assessment of Large-scale Power Systems to False Data Injection Attacks

Zhigang Chu, Jiazi Zhang+2 more|arXiv (Cornell University)|May 10, 2017

Smart Grid Security and Resilience26 references3 citations

TL;DR

This paper proposes a modified Benders' decomposition (MBD) algorithm to efficiently evaluate the vulnerability of large-scale power systems to false data injection (FDI) attacks that maximize power flow on target transmission lines. Unlike prior methods reliant on mixed-integer reformulations, MBD avoids binary variables by leveraging duality, enabling scalable solution of attacker-defender bi-level programs on systems with thousands of buses, such as the 2383-bus Polish system, and revealing that congested lines are highly vulnerable to overflow attacks.

ABSTRACT

This paper studies the vulnerability of large-scale power systems to false data injection (FDI) attacks through their physical consequences. Prior work has shown that an attacker-defender bi-level linear program (ADBLP) can be used to determine the worst-case consequences of FDI attacks aiming to maximize the physical power flow on a target line. This ADBLP can be transformed into a single-level mixed-integer linear program, but it is hard to solve on large power systems due to numerical difficulties. In this paper, four computationally efficient algorithms are presented to solve the attack optimization problem on large power systems. These algorithms are applied on the IEEE 118-bus system and the Polish system with 2383 buses to conduct vulnerability assessments, and they provide feasible attacks that cause line overflows, as well as upper bounds on the maximal power flow resulting from any attack.

Motivation & Objective

• To address the scalability limitations of existing methods for evaluating false data injection (FDI) attacks in large power systems.
• To develop a general-purpose algorithm that solves attacker-defender bi-level linear programs (ADBLPs) without converting them to mixed-integer linear programs (MILPs).
• To assess the vulnerability of large systems—specifically the IEEE 118-bus and 2383-bus Polish systems—to FDI attacks targeting line overflow.
• To investigate how overall system congestion influences the severity and feasibility of FDI attacks.
• To provide actionable insights for system operators to improve resilience through targeted line limits and measurement protection.

Proposed method

• Proposes a modified Benders’ decomposition (MBD) algorithm that transforms the attacker-defender bi-level linear program (ADBLP) into a single-level problem using duality theory.
• Uses duality to replace the second-level optimal power flow (DCOPF) with its KKT conditions, avoiding the need for binary variables in the reformulation.
• Solves the resulting problem via a sequence of standard linear programs, enabling scalability to large systems with thousands of buses.
• Applies the MBD algorithm directly to the ADBLP without prior conversion to a mixed-integer program, preserving computational tractability.
• Employs a column-and-constraint generation approach to iteratively refine the master problem and cut generation, ensuring convergence to the optimal solution.
• Validates the method on the IEEE 118-bus and 2383-bus Polish systems under varying attack resource constraints and congestion levels.

Experimental results

Research questions

• RQ1 Can the modified Benders’ decomposition algorithm solve large-scale attacker-defender bi-level programs without converting them to mixed-integer linear programs?
• RQ2 How does the vulnerability of transmission lines to false data injection attacks vary with system congestion levels?
• RQ3 Which lines in large power systems are most susceptible to overload under FDI attacks, and what structural features make some lines immune?
• RQ4 To what extent do attack resource constraints (e.g., l1-norm of load shifts) affect the maximum achievable power flow on target lines?
• RQ5 Can the proposed method provide tighter bounds on attack consequences than existing approaches like row generation or difference maximization?

Key findings

• The modified Benders’ decomposition (MBD) algorithm successfully solves the ADBLP for the 2383-bus Polish system, overcoming the intractability of mixed-integer reformulations and prior algorithms like row generation and row-and-column generation.
• Lines that are congested or heavily loaded pre-attack are highly vulnerable to FDI-induced overflows, with nearly all such lines susceptible under optimal attack strategies.
• Radial lines—such as line 176 in the IEEE 118-bus system—remain immune to overflow attacks due to their structural configuration, which inherently prevents power flow from exceeding line limits.
• Even non-congested lines, such as line 141 in the IEEE 118-bus system and line 2110 in the Polish system, can be overloaded under FDI attacks, indicating broader vulnerability than previously assumed.
• As overall system congestion increases (via higher line ratings), the maximum achievable power flow on a target line under attack also increases, indicating that less congested systems may be more vulnerable to the same attack resources.
• The l1-norm of the attack vector serves as a valid proxy for the l0-norm (number of controlled buses), and increasing load shift capacity reduces the number of buses needed to launch a successful attack, revealing a trade-off between detectability and resource usage.