Stability reserve in stochastic linear systems with applications to power systems

This paper studies linear systems under sustained random perturbations with the purpose of defining a stochastic stability reserve, i.e., of computing for a given size of the perturbation the values of the system parameters for which the system shows the best stability behavior. The stochastic perturbation model is given by a bounded Markov diffusion process. The Lyapunov exponent is used for computing the stability reserve. This paper presents a short description of four numerical methods for the computation of the Lyapunov exponent and the methodology is applied to linear oscillator in dimension 2 and to a one machine - infinite bus electric power system.