In many large engineering systems it is important to maintain the system state at an acceptable operating point in the face of random disturbances. For power system analyses, evaluation of the effect of small random load variations has relied on examining the behavior of the linearized system about the operating point of interest. However, results on large deviation phenomena in stochastic differential equations indicate that under certain conditions, such linearized analysis may not be adequate. While the linearized system (without the random disturbance) may be asymptotically stable, the presence of the disturbance causes the state to behave as a diffusion process, "wandering" about the equilibrium. If the region of attraction for the stable equilibrium in the nonlinear system has a portion of its boundary sufficiently close to the equilibrium, the state may eventually leave the attracting set. The deterministic dynamics then dominate, pushing the state away from the desired operating point, resulting in a "large deviation." This research will apply recent theoretical results on large deviations in randomly perturbed dynamical systems to the power system security assessment problem. A primary goal will be to develop a measure which indicates vulnerability to voltage collapse, an observed large deviation effect for which standard small disturbance stability analyses are inadequate.
