Analyzing and Quantifying the Effect of $k$-Line Failures in Power Grids

Contingency analysis in power grids is one of the most effective ways to improve grids' resilience against failures. The main goal of contingency analysis is to detect probable failures in the grid that result in a critical state and deploy preventive measures to avoid such a state. Due to the large number of possibilities, however, high-order contingency analysis is computationally expensive and not fully deployed. In order to circumvent this issue, we analytically compute the redistribution of power flows following a k-line failure (i.e., failures in k distinct lines) using the dc power flow model and based on that introduce the disturbance value of a k-line failure. We show that this value can be efficiently computed in O(1) for any set of line failures independent of the size of the grid and can be effectively used to filter out noncritical contingencies. The disturbance value can, therefore, significantly reduce the time complexity of contingency analysis by revealing contingencies that are vital for more in depth analysis and pave the way for the deployment of high-order contingency analysis in power grids.