基于子模优化的受控孤岛划分与重连及其稳定性保证
Controlled Islanding and Reconnection with Stability Guarantees via Submodular Optimization
- Washington University in St. Louis（华盛顿大学圣路易斯分校）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文针对大规模网络化系统，提出一种基于子模优化的两阶段受控孤岛划分与重连方法，通过李雅普诺夫条件保证稳定性，并开发带反例细化的局部搜索算法，数值实验验证了其有效性。
中文摘要 AI 辅助
在大规模网络化动态系统中，局部故障或扰动可能通过互联传播，从而危及整个网络的稳定性。将网络划分为互不相交的子系统（即孤岛）可以通过隔离网络中不稳定的部分与保持稳定的部分来限制这种传播。本文研究了一个两阶段的受控孤岛划分与重连问题。在第一阶段，网络被划分为稳定和不稳定的孤岛。在第二阶段，选定的稳定孤岛被重新连接，以恢复孤岛划分过程中失去的连通性，同时满足稳定性要求。我们为这两个阶段推导了基于李雅普诺夫的充分条件。为了解决孤岛划分与重连决策之间的耦合问题，我们构建了一个增广图，在该图上，图拟阵的基恰好诱导出所有可容许的孤岛划分与重连对。我们进一步证明了所得到的优化问题等价于一个非增的超模公式。基于这一结构，我们开发了一种带有反例细化的局部搜索算法，并为其在固定样本集上的内循环建立了性能保证。对线性网络系统的数值研究展示了所提出的方法，考察了其对故障位置的敏感性，并在解质量和计算性能方面将所提方法与混合整数线性规划基准进行了比较。
英文摘要
In large-scale networked dynamical systems, local faults or disturbances may propagate through the interconnections and compromise the stability of the entire network. Partitioning the network into disjoint subsystems, or islands, limits this propagation by isolating unstable portions of the network from those that remain stable. This paper studies a two-stage controlled islanding and reconnection problem. In the first stage, the network is partitioned into stable and unstable islands. In the second stage, selected stable islands are reconnected to recover connectivity lost during islanding while satisfying stability requirements. We derive Lyapunov-based sufficient conditions for both stages. To address the coupling between the islanding and reconnection decisions, we construct an augmented graph on which the bases of a graphic matroid induce exactly the admissible islanding and reconnection pairs. We further show that the resulting optimization problem admits an equivalent nonincreasing supermodular formulation. Based on this structure, we develop a local-search algorithm with counterexample refinement and establish a performance guarantee for its inner loop with fixed sample sets. Numerical studies on linear networked systems illustrate the proposed procedure, examine its sensitivity to fault locations, and compare the proposed method with a mixed-integer linear programming benchmark in terms of solution quality and computational performance.
