Multilevel cascaded H-bridge (CHB) converters, with a three-phase PWM rectifier as each power unit, are widely used as the grid-side converters in the medium and high voltage drive system. When the CHB converter is accessed into the grid, the low frequency oscillation (LFO) may occur. It impacts the safety and stability of the system. In order to discuss this problem, the time domain and the frequency domain stability analysis with impedance modeling are adopted. Firstly, the dq-frame impedance and harmonic linearized impedance modeling of the medium voltage drives are deduced, and the relationship between the two modeling is discussed. The impedance is measured to verify the modeling accuracy. Then, the LFO is reproduced by time domain simulation, and the influencing parameters of system stability are given intuitively. Finally, with the generalized Nyquist stability criterion (GNSC), the critical stability condition of the system is given. Simulation results and frequency domain analysis results have verified the accuracy of the impedance modeling and the effectiveness of the stability analysis. The LFOs can be suppressed by modifying the parameters of the rectifier voltage loop, current loop and phase-locked loop (PLL).