Study On Nonlinear Dynamics In Power System Under Noise Perturbation

Steady operation of power systems has become more imminent in present day as most of the modern power system networks are being operated under highly stressed conditions due to economic and environmental constraints. Over the past few years, nonlinear dynamics in power system has been received attention. However, to my best knowledge, in those previous studies, the effect of the noise excitation on the nonlinear dynamics in power system is not considered. In fact, noise is unavoidable for open systems which are subject to external constraints and perturbation. On the other hand, it is well-known that noise has profound effects on the behavior of nonlinear systems and can lead to many counterintuitive phenomena. In recent years, the study of nonlinear dynamical systems perturbed by noise has attracted the attention of an increasing number of researchers due to its potential technological applications. The main aim of this work is to investigate how noise excitation affects nonlinear dynamics in power system. The main research work of this dissertation has five parts as follows:First, give a brief introduction about current study on nonlinear dynamics in power system and stochastic dynamics in typical nonlinear system, and then expound systematically the the several methods for investigating the stochastic bifurcation and stochastic chaos, such as Melnikov founction, phase diagram, power spectra, the largest Lyapunov exponent, erosion of safe basin,etc., finally point out the aim and significance of this dissertation.Second, chaotic responses of power system under load perturbation and bounded noise excitation is investigated by analytics method and numerical simulations. The Melnikov method is applied to obtain the necessary condition for the rising of chaos. It is found that for the deterministic system when the strength of load perturbation is greater than a threshold, the Smale's chaos in power system occurs. More significantly, it is found that with random bounded noise the threshold of load perturbation for the onset of chaos is reduced, that is, bounded noise will make it easier to induce and enhance chaos in power system, which is further verified by the maximal Lyapunov exponents of the system.Third, the dynamical behaviors of single-machine infinite-bus (SMIB) power systems dependence on random parameter (namely, noise-perturbed parameter) is studied. It is found that when the parameter perturbations is weak, chaos is absent in power systems. With the intensity of random parameterσincreasing, power systems become unstable and fall into chaos asσis further increased. Fourth, we study how random phase (namely, noise-perturbed phase) effects the dynamical behaviors of power systems. The studied model is described by the classical SMIB system which operate in a stable periodic regime far away from chaotic behavior. It is found that when the phase perturbations is weak, chaos is absent in power systems. With the disturbed intensityσincreasing, power systems become unstable and fall into chaos asσis further increased. These phenomena imply that random phase can induce and enhance chaos in power systems.Fifth, we investigate how the noise effect the dynamics of power system and complex power network. It is found that, with certain strength of noise, chaos in power system was induced and voltage collapse was taken place in complex power network. Our results may provide a useful tip for understanding the stochastic dynamics of power system and help to maintain the power system's security operation.