Line failure probability bounds for power grids
  We develop upper bounds for line failure probabilities in power grids, under the DC approximation and assuming Gaussian noise for the power injections. Our upper bounds are explicit, and lead to characterization of safe operational capacity regions that are convex and polyhedral, making our tools compatible with existing planning methods. Our probabilistic bounds are derived through the use of powerful concentration inequalities. 
Tommaso Nesti, Alessandro Zocca, Bert Zwart
cs.SY math.OC math.PR