基于群特性分析的DC-DC变换器级联系统稳定性判据

摘要

Stability analysis about cascaded system of power converters is an unsolved problem yet, the impedance ratio criteria applied in linear circuits is not suitable for analysis and study on cascaded systems of switched circuit. Therefore, this paper introduces group theory which researches symmetry into analysis of cascaded system of DC-DC converters, defines their group set, discusses their group characteristics, reveals the relationship and physical significance between their group and cascade characteristics. As a result, this paper develops a stability criterion about cascaded system of DC-DC converters based on group characteristics, gives a novel mathematical tool to solve stability problem of cascaded system of DC-DC converters.%电力电子变换器级联的稳定性分析是一个尚未解决的问题，线性电路的阻抗匹配规律不适合开关电路级联系统的分析和研究。为此，论文尝试将研究对称性的基本理论--群论引入到DC-DC变换器级联系统的分析中，试图根据DC-DC变换器级联系统的物理结构，定义基本DC-DC变换器级联系统的群集合．探讨它们的群特性，揭示群特性与级联特性之间的联系及物理意义，由此初步提出一个基于群特性分析的DC-DC变换器级联系统的稳定性判据，为解决DC-DC变换器级联的问题提供一个新的数学工具。