三相PWM整流器中灾难性分岔分析

Analysis of Catastrophic Bifurcation of Three-phase PWM Rectifier

该文研究了三相PWM整流器由于电路参数的非理想因素而引起的灾难性(catastrophic)分岔。利用状态空间平均模型研究了闭环系统的稳定性,得到了系统状态空间平均模型雅克比(Jacobian)矩阵的特征根轨迹,据此确定了系统的边界,结果表明,交流侧等效串联电阻是影响系统灾难性分岔的一个本质参数。通过分析状态空间平均模型的平衡点,得到一个参数含有交流侧等效串联电阻的一元二次方程,该方程Δ=0所确定的边界,恰好与状态空间平均模型得到的边界相吻合,但据此确定的关于系统稳定边界的表达式更能反映系统运行的物理机理和本质特性。比较了利用数值仿真、状态空间平均模型、系统功率方程和系统的平衡点4种不同方法分析系统稳定性的优缺点,并提出了一种避免灾难性分岔发生的控制措施。最后,通过数值仿真和电路实验验证了分析结果的正确性。

This paper investigates a catastrophic bifurcation for three-phase PWM rectifiers due to non-ideal parameters. An average state space model is utilized to study stability of the closed loop system, and by analyzing the eigenvalues locus of the Jacobian matrix of the state space averaged model, get the system stability boundary. The results show that the ac equivalent series resistance is a key factor which impacts the catastrophic bifurcation of PWM rectifiers. By analyzing the equilibrium point of the average state space model, a quadratic equation including equivalent series resistance is obtained and the critical value obtained by Δ=0 of the quadratic equation is consistent with the boundary calculated by the average state space model, but the description on stability boundary obtained by this can better reflect the physical mechanism and essential characteristic of the system. A comparison of using numerical simulation, state space averaged model, system power equation and system equilibrium point to analyze system stability has been done and a measurement is proposed to avoid such catastrophic bifurcations. Finally, the simulation and experimental results verified the availability of the analysis.