高阶并联Buck变换器稳定性分析的等效模型

Equivalent Model for Stability Analysis of Higher Order Paralleled Buck Converters

为了能简单而有效地完成高阶并联DC-DC变换器系统的稳定性分析,文中提出了一种能直接求解系统雅可比矩阵特征值的等效模型。文中以采用PI控制的Buck变换器并联系统为研究对象,采用状态转移矩阵并将矩阵系数进行线性化处理,建立了并联系统的简化离散模型。基于简化离散模型,求解了系统的雅可比矩阵。通过矩阵行列式的行、列转换,推导了高阶并联系统稳定性分析的等效模型。利用等效模型,简单而直接地获取了雅可比矩阵特征值的解析解,极大地简化了高阶并联系统的稳定性分析。计算得到了并联系统电压环和电流环控制参数的稳定边界条件。通过将模型计算结果与系统仿真、实验运行结果对比,验证了高阶并联系统稳定性分析模型及控制参数边界条件的有效性。

For enabling simple and effective analysis of stability of high order paralleled DC-DC converters system, a equivalent model is proposed for solving eigenvalue of the Jacobian matrix. Buck paralleled system adopting PI control is considered. The simple discrete model of paralleled system is founded by adopting state transfer matrix and linearizing the matrix coefficients. The Jacobian matrix of system is solved based on the simple discrete model. The equivalent model of stability analysis for high order paralleled system is deduced by rows and columns transformation. The analytical values of eigenvalues could be directly calculated based on the equivalent model, which greatly simplifies the stability analysis of high order paralleled system. The boundary conditions of voltage loop and current loop control parameters are deduced. The validity of stability analysis model and boundary conditions is approved by comparing the calculation results of model with the simulation and experiment results of paralleled system.