基于二阶平均法和Melnikov法准周期负荷扰动电力系统混沌振荡分析

Analysis of Chaotic Oscillation in Power System Under Quasi-Periodical Load Disturbance by Using Second Order Averaging Method and Melnikov Method

电力系统是典型的非线性系统,存在着复杂的非线性动力学行为。本文分析了在准周期负荷扰动下电力系统的混沌振荡,该振荡模型形同准周期驱动的非线性Helmholtz振子。经过适当变换,利用二阶平均法将系统平均化,得到一个周期扰动的Hamilton系统。求出该Hamilton系统的同宿轨道方程后,构建3个Melnikov函数,相应地得到3个产生混沌振荡的阻尼系数阈值。当阻尼系数在这些阈值之间取值时,可能产生6种不同结构混沌形态中的一种混沌振荡。

Power system is a typical nonlinear system and has nonlinear dynamic characteristics, for example, bifurcation, chaos and fractal. In this paper, chaotic oscillation in power system under quasi-periodical load disturbance is analyzed, and the researched model is similar to a quasi-periodically forced Helmholtz oscillator. By proper transformations and using second order averaging method, the system is changed into an averaged system which is a periodically disturbed Hamilton system. The homoclinic orbits of the Hamilton system are formulated and three Melnikov functions are constructed, and therefore three thresholds of damp coefficient for chaotic oscillation are obtained. If the damp coefficient is between the thresholds, one of six structurally different types of chaotic oscillation behavior may happen.