Single-phase four quadrant converter is an important part of high-speed train traction drive system. High-speed train and power supply system coupling form the high-speed rail system. Focusing on the medium-frequency oscillation phenomenon between the AC power supply system and high-speed trains, this paper considers digital control delay effects in 4Q converter modeling and analysis. It presents a mathematical model for a single-phase 4Q converter, coupling with the power supply system impedance, and it uses Hopf bifurcation theory of nonlinear systems, small disturbance method and the root-locus method to study on AC power railway system stability, especially on the system stability with different circuit parameters and control parameters. The numerical simulation results and the experiments on the small scale prototype hardware platform have verified the theoretical analysis.