耗散性非自治电路的确定与不定解  

The definite and indefinite-solutions in the dissipative non-autonomous circuits

作　　者：黄炳华[1] 陈新苗[1] 韦善革[1] HUANG Binghua;CHEN Xinmiao;WEI Shan’ge(School of Electrical Engineering,Guangxi University,Nanning 530004)

机构地区：[1]广西大学电气工程学院,南宁530004

出　　处：《电气技术》2022年第9期54-68,共15页Electrical Engineering

基　　金：国家自然科学基金(60662001)非线性微分方程基础上的功率平衡。

摘　　要：谐波平衡原理只能求非线性动态系统进入稳态的振荡解,无法求出起始暂态过程,由于没有引入初始条件,它无法求出自振荡分量的初始相角。关于谐波分析法,如果最初谐波项的假设能够符合被求电路的物理实际,会得到有实数解的正确结果。反之实数解的缺失,说明初始假设不合理。为此必须重新设定谐波的形式。二阶非自治电路含有自激和受迫两个谐波分量,是一个耦合振荡。本文论述五次方项的非自治电路,用等效基波电导替代非线性阻尼,可将简化的网络划分成为两个分部,各分部有各自单独的振荡频率,可以单独列出微分方程而后联合求解。分部网络的功率各自独立维持平衡,是求解非自治电路的有效方法,有广泛的普遍性和适用性。The harmonic balance principle can only seek the stable oscillation solution of non-linear dynamic system,but it cannot solve the initial transient process.Since the initial condition is not introduced,the initial phase angle of the self-excited oscillation component cannot be obtained.Concerning harmonic analysis method,if the initial assumption of the harmonic components fits the physical characteristics of the circuit,the correct real number solution will be obtained.By contrast,the absence of real number solution implies an improper initial assumption.In this case,to reset the form of harmonic components is necessary.Containing both self-excited and forced oscillation components,the second order non-autonomous circuit is a coupled oscillation.The non-autonomous circuits of fifth power are discussed in this paper.The non-linear damping factor can be replaced by equivalent first wave conduction.The simplification network can be divided into two subsections,each of which possess independent oscillation frequency.The differential equation can independently be described and then be solved together.The power balance of each subsection network must be maintained.It is an effective way to solve non-autonomous circuits.It possesses widely universality and applicability.

关 键 词：谐波分析 非自治电路 非线性振荡 耦合 初相位 

分 类 号：TM13[电气工程—电工理论与新技术]