Dynamical reliability of the stochastic power systems with discrete random variability

In this paper a novel method is presented to analyze the dynamical reliability of the stochastic power systems with discrete random variability. It is inevitable for the power systems to suffer from external stochastic disturbance. At the same time, the components’ failure will bring abrupt changes in their substructures, which can be considered as the internal stochastic disturbance. It is demonstrated that the components’ failure performs random jumpy factors switching between a finite number of modes. This salient feature allows us to identify this type of dynamic behavior as the response of the hybrid power systems undergoing Markovian jumps. Utilizing a two-step approximate technique, the considered multi-DOF hybrid system can be reduced to a one-dimensional averaged Itô equation of the form of the system’s total energy. The approximate analytical solution of the associated back Kolmogorov equation of the system’s energy is derived to predict the dynamical reliability of the original hybrid systems.