The utilization of synchronous machines in electric power systems as central generators and in electric drive applications as high-performance motors makes their modeling, simulation, state estimation, and analysis important in many scenarios; however, the multiple time-scale nature of the associated dynamic model, coupled with the presence of noise, complicates traditional methods.We approach the problem in this work through dimensional reduction in nonlinear filtering. This can be understood as a combination of filtering and averaging. Recent advances in the development of particle filters are applied to the Single Machine Infinite Bus (SMIB) seven dimensional model of a synchronous generator and to the specific problem of a line contingency. Excellent system tracking coupled with significant computational savings are achieved.In addition to system tracking, the traditional deterministic methods currently used in industry to quantify system stability are looked at from a Random Dynamical Systems (RDS) perspective. The maximal Lyapunov exponent (MLE) for a two dimensional model of a synchronous generator is calculated analytically to account for multiple white noise forcing elements. The ``real" or colored noise case is also considered and an analytic expression derived.Further, the presence of resonant zones and their stability for a two dimensional swing model is established. The stability of these zones is looked at from the Large Deviations perspective and is facilitated through an understanding of the Mean Exit Time. Numerical procedures are developed to calculate the Most Probable Exit Path along which; rare, long time transitions take place.
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