Abstract:

Based on constraint Euler-Lagrange equations, a general dynamic model is presented for power converters with multiple or single switches. From the research on the energy of power converters, the generalized charges and generalized currents coordinates of dynamic elements are chosen, switching function is introduced, and a set of differential algebraic equations with constraint can be obtained based on Euler-Lagrange equations with the Kirchhoff’s current constraints. The inductor currents and the capacitor voltages are chosen as the state variables, and then the state equations of the converters can be got ultimately. The proposed method is applied to model an ?uk converter circuit with an ideal switch and a three phase PWM rectifier with multiple switches. From the modeling process, it can be seen that this method is unified, clear in physical meaning and strong commonality. Finally, with the obtained state equations, the working process of ?uk converter is simulated in MATLAB, the simulation results coincide with the operation of the power converter, and it verify the effectiveness of the proposed method, which has higher application value to model the more complex power converters.

Key words: power converter, Euler-Lagrange equation, modeling, simulation

摘要：

基于约束拉格朗日方程, 提出一种通用的适合具有开关的电力变换器的动力学模型。从研究电力变换器的能量出发, 选择动态元件的广义电荷和广义电流坐标, 引入开关函数, 运用电力变换器受基尔霍夫电流约束的欧拉?拉格朗日方程, 可以得到一组带有约束的微分代数方程。选取电感电流和电容电压作为状态变量, 可以得到含有开关函数的状态方程模型, 并将此建模方法应用于单开关的 ?uk 型变换器和多个开关的三相三线 PWM 整流器的建模分析中。从建模过程可以看出, 此方法步骤清晰统一, 物理意义明确, 通用性强。最后, 利用得到的状态方程模型, 在 MATLAB 中对 ?uk 型变换器工作过程进行仿真计算, 仿真结果与电力变换器的运行情况吻合, 说明了建模方法的有效性, 对于更复杂的电力变换器的建模分析也具有较高的应用价值。

关键词: 电力变换器, 欧拉-拉格朗日方程, 建模, 仿真