基波谐振串联铁磁电路的稳态频域近似分析

On the Frequency-Domain Steady-State Analysis of Series Ferroresonant-Circuits

本文采用适用于强非线性高阶微分方程的等效小参量法,对基波谐振串联铁磁电路作稳态频域近似分析。解答由主部x_0(只包含一个基波分量)和一、二阶修正量x_1、x_2(三次、五次谐波分量及基波分量的修正量)组成。提出了一种求解解答主部x_0的图介方法,可直接得出磁链幅值及相位随电源电压值的变化曲线,能显示出电路的全局性状可与数值计算方法起互补作用。示例表明,以上方法简单实用,计算结果(I、U_L有效值及一、三次谐波分量)与EMTP程序的计算结果接近。

In the paper the equivalent small-parameter method, suitable for strongly nonlinear systems, is used for frequency- domain steady-state analysis of series ferroresonant circuits. The solution is composed of the main oscillation x0 (includes one resonant-frequency component only) and 1st-, 2nd-order corrections x1, x2 (3rd, 5th harmonics and correction of the fundamental-frequency component). A new diagrammatic method for determining the main oscillation x0 is recommended, which gives directly the curves of the amplitude and phase of flux verses source voltage, demonstrating the global behavior of the circuit. The proposed methods are simple and practical, and also may form the complement to numerical methods. Their results meet well with those calculated by EMTP program.