Study of bifurcation and low-frequency oscillation in voltage-controlled SEPIC converters

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.