A Mixed Integer Programming Model for Evaluating the Hidden Probabilities of $N$ - ${k}$ Line Contingencies in Smart Grids

In contingency analysis of large-scale power systems, the high-order contingencies involving a relatively large number of component failures are traditionally assumed to have a very low occurrence probability. However, this may underestimate the probability of some N-k contingencies and thus pose risk to the reliable system operations considering that those contingencies would cause severe consequences. In this paper, we investigate the problem of hidden N-k contingencies and cast the problem of evaluating the hidden probability of an N-k contingency as a mixed integer linear programming problem. The simulation results on the IEEE 14-bus and 118-bus systems verify the effectiveness of the proposed model.