This paper presents the research and implement of the three-phase converter control system under unbalanced grid conditions. The well-known PWM techniques applied in the unbalanced converter control system are the sinusoidal pulse-width modulation, hysteresis current control and the space vector modulation, etc. However, the linear modulation range of the sinusoidal pulse-width modulation and hysteresis current control are only 1.0. The hysteresis current control method is limited to specific control configuration, furthermore, the current harmonics are variable and it is difficult to design the filter. The linear modulation range of the space vector modulation is up to 1.1547, and the null-vectors placement in space vector modulation converter are arranged under three-phase consideration, thus the null-vector can be cancelled in the line-to-line voltages on the unbalanced system. A generalized pulse-width modulation system and a closed looped control system are proposed for connected with three-phase unbalanced power system; the simulation results and experimental results are presented in this paper to validate the theoretical analysis, as well.