车用永磁同步电机稳定性分析

Stability Analysis of Permanent Magnet Synchronous Motor in Vehicle

采用多参数统一方法,将永磁同步电机数学模型中多个参数变化的特性综合到两个参数的变化上,给出了平衡点的稳定性判别条件,推导了平衡点产生Hopf分岔及叉形分岔的条件。仿真分析了永磁同步电机的平衡点随这两个参数变化的规律,得到了平衡点的叉形分岔点以及亚临界Hopf分岔点。分析得到了永磁同步电机中的不同动力学现象,解释了不同动力学现象产生的机理。

Since the permanent magnet synchronous motor（PMSM） has a large number of parameters and the direct analysis of parameters＇ impact on PMSM＇s dynamic behaviors is inconvenient, multi-parameter unified approach was proposed and all the PMSM＇ s dynamic behaviors can be discovered through in-depth analysis of the unified parameters. PMSM equilibrium local stability condition as well as Hopf bifurcation condition and pitchfork bifurcation condition were derived through the Routh- Hurwitz criterion and the bifurcation theory respectively. Pitchfork bifurcation line together with subcritical Hopf bifurcation line divided the equilibrium parameter plane into three regions, where the equilibrium had different characteristics in different regions. Simulation showed the equilibrium bifurcation characteristics along with single parameter variation, and one pitchfork bifurcation point and two subcritical Hopf bifurcation points were found in the equilibrium bifurcation curve. The PMSM dynamic behaviors along with parameters variation were studied by phase portraits, time history map and Poincar~ bifurcation diagram , and presented different mechanisms. If there was only one stable equilibrium in the parameters regions, the PMSM can work stably. If there were two stable equilibriums in the parameters regions, the initial conditions would affect PMSM operation. If there was no stable equilibrium in the parameters regions, the PMSM cannot work stably. The research of this paper can provide some references for PMSM design.