考虑滤波环节寄生电阻的三相电压型逆变器的数学模型分析

针对三相电压型逆变器这个时变的、耦合的、多输入、多输出的开关型非线性系统,应用开关函数建立了考虑滤波环节寄生电阻的系统数学模型,引入开关周期平均算子将时变的系统转化为连续系统,建立了系统的大信号动态数学模型,同时应用小信号扰动法建立了系统的小信号数学模型,得出从占空比输入到逆变器输出的传递函数。讨论了大小信号模型的适用范围,分析了小信号模型中寄生电阻对系统频率特性的影响。理论分析和仿真结果表明,不考虑寄生电阻理想情况下的逆变器稳定性能差于考虑寄生电阻的非理想逆变器。因此,在分析逆变器稳定性能和闭环设计过程中,可优先考虑理想情况下的逆变器数学模型。

Analysis of the mathematic model for three-phase voltage source inverter relating to filter autoecious resistance

The three-phase voltage source inverter is a switch with nonlinear system,featuring time-var-ying,coupling,multi-input and multi-output,The mathematical model relating to filter autoecious resistance is established with switching function. The time-varying system is transformed into the continuous system with the average switch period operator. The big signal dynamic mathematical model is established. The small signal dynamic mathematical model is established with the small signal perturbation method. The transfer functions from occupancy rate input to inverter output are obtained. The applicability range of the big and small signal dynamic mathematical model is discussed. The effects of autoecious resistance on frequency characteristic of the small signal dynamic mathematical model are analyzed. The theoretical analysis and simulation results show that the stabilization of inverter without regard to autoecious resistances is worst than it with. Therefore , when we analyze stabilization performance and design close-loop,the ideal mathematical model of inverter should be elected firstly.