A class of power network reliability problems via colored noise modeling

The stochastic model of a two-dimensional system represented by a synchronous machine connected to an infinite bus and perturbed by a colored noise is described. The solution of the model determines the mean first passage time of the system from the domain of attraction of its equilibrium point as a function of the magnitude of the perturbation as well as its bandwidth. Based on the type and the size of a perturbation, the approach can be used in a power network to reduce the level of uncertainty which inherently exists in stability studies due to the random variation of system parameters.<>