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Cascading failures typically occur following a large disturbance in power systems, such as tripping of a generating unit or a transmission line. Such failures can propagate and destabilize the entire power system, potentially leading to widespread outages. One approach to mitigate impending cascading failures is through controlled islanding, in which a set of transmission lines is deliberately tripped to partition the unstable system into several disjoint, internally stable islands. Selecting such a set of transmission lines is inherently a combinatorial optimization problem. Current approaches address this problem in two steps: first, classify coherent generators into groups and then separate generator groups into different islands with minimal load-generation imbalance. These methods, however, are based on computationally expensive heuristics that do not provide optimality guarantees. This paper proposes a novel approach to controlled islanding based on weak submodularity. The new formulation jointly captures the minimal generator non-coherency and minimal load-generation imbalance in one objective function. The islanding problem is then relaxed to a formulation with bounded submodularity ratio and a matroid constraint. An approximation algorithm is proposed which achieves a provable optimality bound on non-coherency and load-generation imbalance. The proposed framework is tested on IEEE 39-bus and 118-bus power systems. [ABSTRACT FROM AUTHOR]

Voltage instability occurs when a power system is unable to meet the reactive power demand, and is typically corrected by switching on additional reactive power devices such as capacitor banks. Real-time monitoring and communication technologies can potentially improve voltage stability by enabling the rapid detection of low voltages and the implementation of corrective actions. These corrective actions, however, will only be effective in restoring stability if they are chosen in a timely, scalable manner. In this paper, we propose a submodular optimization approach for designing a control strategy that prevents voltage instability. Our key insight is that the voltage deviation from the desired level is a supermodular function of the set of reactive power injections that are employed, leading to computationally efficient control algorithms for stabilization with provable optimality guarantees. This submodular control framework is tested on the IEEE 300-bus transmission system. [ABSTRACT FROM PUBLISHER]