Abstract This paper examines the effects of reactive power dispatch, losses, and voltage profile on the results of the interdiction model to analyze the vulnerability of the power system. First, an attacker-defender Stackelberg game is introduced. The introduced game is modeled as a bilevel optimization problem where the attacker is modeled in the upper level and the defender is modeled in the lower level. The AC optimal power flow (ACOPF) is proposed as the defender’s tool in the lower-level problem to mitigate the attack consequences. Our proposed ACOPF-based mathematical framework is inherently a mixed-integer bilevel nonlinear program (MIBNLP) that is NP-hard and computationally challenging. This paper linearizes and then transforms it into a one-level mixed-integer linear program (MILP) using the duality theory and some proposed linearization techniques. The proposed MILP model can be solved to the global optimum using state-of-the-art solvers such as Cplex. Numerical results on two IEEE systems and Iran’s 400-kV transmission network demonstrate the performance of the proposed MILP for vulnerability assessment. We have also compared our MILP model with the DCOPF-based approach proposed in the relevant literature. The comparative results show that the reported damage measured in terms of load shedding for the DCOPF-based approach is always lower than or equal to that for the ACOPF-based approach and these models report a different set of critical lines, especially in more stressed and larger power systems. Also, the effectiveness and feasibility of the proposed MILP model for power-system vulnerability analysis are discussed and highlighted.

中文翻译：

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基于ACOPF的电力系统脆弱性评估双层优化方法

摘要 本文研究了无功功率调度、损耗和电压分布对阻断模型结果的影响，以分析电力系统的脆弱性。首先，介绍了攻击者-防御者 Stackelberg 博弈。引入的游戏被建模为一个双层优化问题，其中攻击者在上层建模，防御者在下层建模。交流最优潮流（ACOPF）被提议作为防御者在较低级别问题中的工具，以减轻攻击后果。我们提出的基于 ACOPF 的数学框架本质上是一个混合整数双层非线性程序 (MIBNLP)，它是 NP 难的并且在计算上具有挑战性。本文使用对偶理论和一些提出的线性化技术对其进行线性化，然后将其转换为一级混合整数线性规划 (MILP)。可以使用最先进的求解器（例如 Cplex）将所提出的 MILP 模型求解为全局最优解。两个 IEEE 系统和伊朗 400 kV 传输网络的数值结果证明了所提议的 MILP 用于脆弱性评估的性能。我们还将我们的 MILP 模型与相关文献中提出的基于 DCOPF 的方法进行了比较。比较结果表明，基于 DCOPF 的方法根据减载测量报告的损坏始终低于或等于基于 ACOPF 的方法的损坏，并且这些模型报告了一组不同的临界线，尤其是在压力更大和更大的电力系统。还，