VIBRATONAL MECHANICS AND STOCHASTIC QUASI-RESONANCES

The concept of vibrational mechanics was pioneered in the works by Professor I.I. Blekhman and developed by his numerous disciples and coleagues. It is a powerful tool for the study of such systems with fast excitations, in which slow motion is of primary interest. One important application of this approach is the stochastic resonance, the phenomenon of resonance-like response of slow variables to intensity of stochastic excitation. This phenomenon is considered within the framework of vibrational mechanics as forced lowfrequency oscillations near the natural frequency, which evolves under the influence of changing high-frequency stochastic excitation. We propose a generalization of this approach to the case when the evolution of low-frequency properties of the system leads not to the equality of the natural frequency and the frequency of the external slow force, but to the loss of stability in a certain interval of the stochastic excitation intensity. Since in this case, as for stochastic resonance, the external manifestation of the process is the resonance-like response of the system, the considered effect can be called stochastic quasi-resonance, As an example, we consider a rotor with anisotropy of bending stiffness under the action of stochastic angular velocity oscillations.

Linearization threshold condition and stability analysis of a stochastic dynamic model of one-machine infinite-bus (OMIB) power systems

With the increase in the proportion of multiple renewable energy sources, power electronics equipment and new loads, power systems are gradually evolving towards the integration of multi-energy, multi-network and multi-subject affected by more stochastic excitation with greater intensity. There is a problem of establishing an effective stochastic dynamic model and algorithm under different stochastic excitation intensities. A Milstein-Euler predictor-corrector method for a nonlinear and linearized stochastic dynamic model of a power system is constructed to numerically discretize the models. The optimal threshold model of stochastic excitation intensity for linearizing the nonlinear stochastic dynamic model is proposed to obtain the corresponding linearization threshold condition. The simulation results of one-machine infinite-bus (OMIB) systems show the correctness and rationality of the predictor-corrector method and the linearization threshold condition for the power system stochastic dynamic model. This study provides a reference for stochastic modelling and efficient simulation of power systems with multiple stochastic excitations and has important application value for stability judgment and security evaluation.