We study rare failures associated with cleared faults in the transmission level power system dynamics described by swing equations. We assume that (a) prior to a fault, which may occur at random at any line, the system was in a balanced state; (b) fault is cleared within a few seconds; (c) a failure is counted at a power line of the system if during the post-fault transient (before or after the fault is cleared) power flow along the line exceeded a safe limit.  The goal of this project is to develop a procedure to understand, estimate and analyze the dynamics of any given power grid that satisfies the linear swing equations. We are looking for a way to determine the distribution of the magnitude of the overloading of the system over time. This way we can determine how reliable and stable the system is even if there are failures in the grid for a random period of time.