Towards Scalable Voltage Control in Smart Grid: A Submodular Optimization Approach

Voltage instability occurs when a power system is unable to meet reactive power demand at one or more buses. Voltage instability events have caused several major outages and promise to become more frequent due to increasing energy demand. The future smart grid may help to ensure voltage stability by enabling rapid detection of possible voltage instability and implementation of corrective action. These corrective actions will only be effective in restoring stability if they are chosen in a timely, scalable manner. Current techniques for selecting control actions, however, rely on exhaustive search, and hence may choose an inefficient control strategy. In this paper, we propose a submodular optimization approach to designing a control strategy to prevent voltage instability at one or more buses. Our key insight is that the deviation from the desired voltage is a supermodular function of the set of reactive power injections that are employed, leading to computationally efficient control algorithms with provable optimality guarantees. Furthermore, we show that the optimality bound of our approach can be improved from 1/3 to 1/2 when the power system operates under heavy loading conditions. We demonstrate our framework through extensive simulation study on the IEEE 30 bus test case.