基于非线性振荡和混沌分析的单相AC-DC变流电路的摄动解析

摘要

This paper deals with the issue of modeling method by perturbation solution to the single-phase AC-DC converter. A continuous circuit that includes a single-phase AC-DC converter is inducted first. And then a differential equation is presented with two parameters, which are controlling parameter and small perturbation parameter. A strict proof indicates that this equation can be solved by the regular perturbation. The compareison between the result and the simulation figures of PSCAD/EMTDC, shows that the result is correct and simple, thus avoiding the requirements for large computation capacity. Finally, the physical significance of the two parameters is analyzed, showing that they may incur the period-doubling chaos. This method not only fits the single-phase AC-DC converter circuit, but also meets the need of two-phase or N-phase circuits.%针对单相交直流全桥变流电路，推导出其在脉宽调制下的连续等效摄动解析模型．首先通过研究非线性振荡过程得到其连续微分方程，该方程含有控制参数和摄动参数．随后通过数学理论证明正则摄动方法能够求出其近似解，求解后对比PSCAD／EMTDC的仿真结果从而验证了解析的正确性．该方法在大规模计算中具有优势．最后分析了控制参数和摄动参数的物理意义，指出这两个参数能够影响变流器的工作状态，甚至引发倍周期混沌．该摄动建模方法不仅适用于单相变流电路，也适用于三相变流电路甚至多相变流电路．