As an indispensable part of traction converter control system, grid synchronization algorithm estimates phase angle of grid to ensure the system work in unit power factor. Second-order generalized integrator frequency-locked loop (SOGI-FLL) algorithm can be used as it has good dynamic response and steady-state accuracy, but its performance dependent on the methods of discretization. Numerical integration methods based on two integrators may cause estimated frequency deviation and orthogonality destruction between output signals. Methods based on discretizing open-loop transfer functions all have accuracy estimated frequency and zero steady-state error, but if the discretization based on discretizing open-loop transfer functions, system is not internally stable. Methods based on discretizing closed-loop transfer functions exhibit steady-state error. These problems will disturb the grid phase calculation, and finally affect the control of traction converter. Comparison of different discretization methods in this paper is by means of transfer functions, bode diagrams, simulations and experiments.