Smart applications supporting modern power systems are susceptible to cyber–physical attacks, particularly False Data Injection attacks that manipulate the input measurements of State Estimation (SE) compromising its output states. This paper proposes an Integer Linear Programming formulation that protects an optimal number of measurement units to prevent cyber–physical attacks, enhancing the robustness of SE. Our approach exhibits low complexity, applies to both linear and nonlinear SE, and converges rapidly toward the optimal solution. The formulation requires information about the grid topology and measurement distribution but does not depend on the power flow equations. Also, the generalized formulation can be customized to consider distinct protection costs for all measurement types, various priorities for different measurements, and a range of measurements and pseudo-measurements. Simulations are performed on the widely used IEEE 14 and 118-bus systems to verify the approach for linear and nonlinear SE and illustrate its practicality.

支持现代电力系统的智能应用程序很容易受到网络物理攻击，特别是虚假数据注入攻击，这些攻击会操纵状态估计（SE）的输入测量，从而损害其输出状态。本文提出了一种整数线性规划公式，可以保护最佳数量的测量单元以防止网络物理攻击，从而增强 SE 的鲁棒性。我们的方法复杂度低，适用于线性和非线性SE，并且快速收敛到最优解。该公式需要有关电网拓扑和测量分布的信息，但不依赖于功率流方程。此外，可以定制通用公式以考虑所有测量类型的不同保护成本、不同测量的不同优先级以及一系列测量和伪测量。在广泛使用的 IEEE 14 和 118 总线系统上进行仿真，以验证线性和非线性 SE 方法并说明其实用性。