Stability, Chaos Detection, and Quenching Chaos in the Swing Equation System

Shun-Chang Chang,Viet-Thanh Pham

doi:10.1155/2020/6677084

Abstract

The main objective of this study is to explore the complex nonlinear dynamics and chaos control in power systems. The rich dynamics of power systems were observed over a range of parameter values in the bifurcation diagram. Also, a variety of periodic solutions and nonlinear phenomena could be expressed using various numerical skills, such as time responses, phase portraits, Poincaré maps, and frequency spectra. They have also shown that power systems can undergo a cascade of period-doubling bifurcations prior to the onset of chaos. In this study, the Lyapunov exponent and Lyapunov dimension were employed to identify the onset of chaotic motion. Also, state feedback control and dither signal control were applied to quench the chaotic behavior of power systems. Some simulation results were shown to demonstrate the effectiveness of these proposed control approaches.

Highlights

Chaotic behaviors in power systems are considered undesirable due to the restrictions they impose on the operating ranges of electrical and mechanical devices. e dynamics of a power system become unstable when they exhibit chaotic motions
Various control algorithms have been presented to control the chaos of power systems [8, 27,28,29,30]. is work proposed converting chaotic behaviors into periodic motions to improve the performance of system dynamics with multiple machine power system chaotic behaviors
A cascade of chaos-inducing period-doubling bifurcations appeared as Kf continued to fall in Figure 2, resulting in a chatter vibration that could cause a voltage collapse, thereby significantly reducing the power system performance and possibly causing catastrophic blackouts

Summary

Introduction

Chaotic behaviors in power systems are considered undesirable due to the restrictions they impose on the operating ranges of electrical and mechanical devices. e dynamics of a power system become unstable when they exhibit chaotic motions. Chaotic motions in a power system were inhibited using state feedback control [21, 31] and dither signal control [32], and the simulation results were Cai et al [21, 31] proposed a simple and effective method for converting chaos into periodic motion at a steady state using the linear-state feedback of an available system variable.

Results

Conclusion