电压型SEPIC变换器中的分岔行为与低频振荡现象分析

Study of Bifurcation and Low-Frequency Oscillation in Voltage-Controlled SEPIC Converters

导出了电压型SEPIC变换器的频闪映射方程,采用数值模拟、非线性动力学理论分析和电路实验的方法研究了系统中的低频不稳定现象,并对不稳定区域中的非线性行为(如准周期分岔、锁相极限环)进行了分析,揭示了低频振荡的特征、振荡周期的变化规律及低频振荡产生的物理机理。结果表明,随着控制器参数的增大,变换器由原来单一的CCM工作模态转化为在CCM和DCM之间间歇性切换的工作模态,是导致系统周期1不动点失稳和系统产生低频振荡的主要原因;低频振荡的出现反映出系统发生了亚临界Hopf分岔;低频振荡周期等于锁相周期态的周期数与锯齿波调制周期的乘积,符合Farey原理。

A stroboscopic map for voltage-controlled single ended primary inductor converters （SEPIC） with pulse width modulation （PWM） is presented, where the low-frequency oscillating phenomena such as quasi-periodic bifurcation and phase locking limit circle occurring in the system are captured by mathematical and experimental methods. According to the bifurcation diagrams and nonlinear dynamical theory, the characteristics of the low-frequency oscillation, the variation rule of the oscillation period as well as the mechanism for the appearance of the low-frequency oscillation are investigated. It is shown that as the controller parameter increases, the change in the conduction mode takes place from the continuous conduction mode （CCM） under the originally stable period one state to the intermittent changes between CCM and discontinuous conduction mode （DCM）, which may be related to the losing stability of the system and brought the system to exhibit low-frequency oscillating behavior in the time domain. Moreover, the occurrence of the low-frequency oscillation reflects that the system may undergo a subcritical Hopf bifurcation, and the oscillation period of the phase locking limit circle is equal to the product of the period of the phase locking state and the PWM period, which agrees with the Farey principles.