一种变压器隔离的双向DC／DC变换器交流小信号模型

变压器隔离的双向DC／DC变换器是混合电动系统中的关键组成部分，由于开关效应引起的非线性特征，使得理论分析与设计双向DC／DC变换器控制系统非常困难。基于双时间尺度理论与状态空间平均法，提出了一种变压器隔离的双向DC／DC变换器的小信号线性模型。根据双时间尺度分解理论，把描述双向DC／DC变换器系统的分段线性方程组分解为快变和慢变子系统，消除慢变子系统中的快变变量得到降阶的慢变子系统。在一个开关周期中，把慢变子系统方程组变换为一个统一的平均值方程，平均值变量分解为一个直流分量与线性的交流小信号变量，直流方程确定了小信号系统的工作点，交流小信号方程是线性的，这使得线性系统理论适用于在一个直流工作点分析、设计非线性的双向DC／DC变换器的控制系统。

A Small Signal Linear Model of Transformer Isolated Bi-directional DC/DC Converter

The transformer isolated bi-directional DC/DC converter is the key component of the traction system in hybrid electrical vehicles（HEVs）. We present a linear mathematic model of transformer isolated bi-directional DC/DC converter for HEVs based on the dual time scale theory and the state space average method. The approximate models are important especially for anal- ysis and closed-loop control design of converter circuits. The differential equations, which govern the converter operation, change periodically among a set of linear differential equations because of the switch effect. Based on the time scale a state variable is decomposed into a fast-scale variable and a slow-scale variable. The fast-scale variable of leakage inductance is eliminated by substituting the fast-scale variable into slow-scale variable equations, resulting in reduced order differential equations. From this set of reduced order differential equations a completely averaged model of the isolated DC/DC converter is derived. The simulation results reveal that the circuit and mathematical model are well consistent. The averaged state variables can be treated as a small component plus a DC component, so the averaged variable can be decomposed into a dynamic small signal part and a DC part. This linear small signal model is suitable for control design and analysis at a steady point which is decided by the DC component. A PI controller is designed with this linear model.