We develop an empirical electrical-based framework to compare between centrality measures as to judge their ability to predict the vulnerability of smart grids and their elements under various attacks. The centrality measures considered are based on a weighted graph adjacency matrix representing the real power flows. The vulnerability is measured by the post-attack unsatisfied load (UL), which is determined through steady-state simulation using the MatPower v6.0. We introduce a generalized vulnerability curve as a plot of measures of electrical damage (e.g., the UL), versus physical damage. We consider various measures of physical damage such as the Fraction of Elements (FOE) removed and sums of centrality scores of elements removed. The area under the vulnerability curve (denoted as VPM) is shown to be a logical, reliable, and consistent indicator of the predictive power of a centrality measure. The VPM is simulated for several attacks including the Remove Most Central Elements First (RMCEF) attack. We show that degree centrality is the most predictive, when compared to eigenvector and betweenness centralities. Moreover, the degree-based RMCEF attack is the worst among the RMCEF and 5400 random attacks. The FOE-degree centrality VPM is the most predictive as well as the most computationally efficient.

我们开发了一个基于经验的电气框架来比较中心性度量，以判断它们预测智能电网及其元素在各种攻击下的脆弱性的能力。所考虑的中心性度量基于表示实际潮流的加权图邻接矩阵。该漏洞是通过攻击后不满意负载 (UL) 来衡量的，该负载是通过使用 MatPower v6.0 的稳态仿真确定的。我们引入了广义脆弱性曲线作为电气损坏（例如，UL）与物理损坏的测量图。我们考虑了各种物理损坏措施，例如移除的元素分数 (FOE) 和移除的元素中心性得分的总和。脆弱性曲线下的区域（表示为 VPM）被证明是合乎逻辑的、可靠的、中心性度量预测能力的一致指标。VPM 针对多种攻击进行了模拟，包括首先删除最中心元素 (RMCEF) 攻击。我们表明，与特征向量和中介中心性相比，度中心性是最具预测性的。此外，基于度的 RMCEF 攻击是 RMCEF 和 5400 随机攻击中最差的。FOE 度中心性 VPM 是最具预测性和计算效率最高的。