In a three phase power system, the voltages at the generation side are in sinusoidal and equal in magnitude with 120? phase difference between the phases. However, at the load side voltages may become unbalanced due to unequal voltage magnitudes at the fundamental frequency, phase angle deviations or unequal distribution of single phase loads. The voltage unbalance is a major power quality issue, because a small unbalance in the phase voltages can cause a larger unbalance in the phase currents. A completely balanced three-phase three wire system contains only positive sequence components of voltage, current and impedance, whereas unbalanced system contains both positive and negative sequence components of voltages and currents. The negative sequence component of current in the unbalanced system increases the temperature and losses in the equipments. Hence, it is necessary to mitigate this problem by supplying the negative sequence current to the load at the load side and keep the source side balanced. This paper proposes the shunt connected, current injecting Distribution Static Synchronous Compensator (DSTATCOM) with appropriate controller to mitigate the unbalanced load current. The symmetrical components based Hysteresis Current Controller (HCC) is designed for DSTATCOM to diminish the unbalances in a three-phase three-wire system. The performance of the controller is studied by simulating the entire system in the MATLAB/Simulink environment. The DSTATCOM with HCC is found to be better than other controllers because it is suitable for compensating both balanced and unbalanced loads.