基于拉格朗日乘子法的虚假数据攻击策略

Injected Attack Strategy for False Data Based on Lagrange Multipliers Method

虚假数据攻击面临掌握的电气参数存在误差,甚至不完整及量测数据中存在不良数据的问题,提出一种基于拉格朗日乘子法的虚假数据攻击策略。首先通过拉格朗日乘子法和增广状态估计法辨识不良数据和估计未知支路电抗,然后在凸松弛技术框架内,将传统的攻击单个量测点的次优虚假数据攻击向量模型转化为基追踪(BP)模型,最后采用交替方向乘子法(ADMM)快速求解次优攻击向量。以典型的IEEE节点测试系统为例进行仿真测试,仿真结果表明:与传统的线性规划算法相比,将攻击单个量测点的次优攻击向量模型转化为BP模型后,采用ADMM求解次优攻击向量具有更高的计算效率;电抗未知支路数量较少时,攻击成功率较高,但是状态变量的误差向量的标准差较小时,电抗未知支路数量对攻击成功率影响减弱;该方法不会显著增加攻击成本。

As there may be errors and incompleteness in electric parameters mastered by attackers, and bad data may also exist in measurements, an injected attack strategy for false data based on Lagrange multipliers method is proposed. First, bad data is identified and unknown branch impedance is estimated by the I.agrange multipliers method and augmented state estimation method, respectively. Then, in the convex relaxation framework, the classic false data injected attack model aimed at attacking an arbitrary specific measurement is transformed into a basis-pursuit （BP） model. Finally, the suboptimum attack vector is quickly solved by alternating the direction method of multipliers （ADMM）. In order to evaluate the strategy, simulations are tested in typical IEEE bus test systems. The results show that ADMM is more efficient than classic linear programming （LP） based on the BP model when the classic false data injected attack model is transformed into a BP model. It is also found that when the number of impedance unknown branches is small, the success rate is relatively high. But when the standard deviation of error vector for state variables decreases, the effect of the quantity of impedance unknown branches on the success rate will be weak. Moreover, this strategy does not significantly increase the attack cost.