Analysing nonlinear oscillation and chaos using fundamental-wave balance principle

Abstract

The fundamental-wave current Is1 can be found by the theory of fundamental harmonic balance. Its flow direc- tion represents profit and loss of active and reactive power in order to maintain self-oscillation, when the exciting source applied to the network is cut off. And it is powerfull basis of judging stability and self-excited oscillation shape and prop- erties. Oscillation frequencyωs and amplitude Um of fundamental- wave solution can be found, when active and reactive power of the network obtain balance synchronously. The respective periodic solution exist inevitably. The universality of the conclusion can be spread to third-order nonlinear differential equation. It is expounded that a differential equation possessing multiple periodic solutions is the important reason of generating chaotic oscillation. Its correctness can be verified by the Simulink.

Keywords

• nonlinear
• stability
• reactive power
• limit cycle
• chaos