The DTSTACOM is a power quality compensator that can be used in distribution grid to compensate the demand of reactive power which can be produced by different linear and nonlinear loads. In this process, the control method of DSTATCOM is one of the key factors to influence the performance of DSTATCOM. This study intent to the effect of two modulation schemes Pulse Width Modulation (PWM) and Hysteresis Current Control (HCC) under several conditions. The proposed modeling approach and Synchronous Reference Frame theory (SRF) are used to verify reactive power compensation and total harmonic distortion (THD). Further to, Pulse Width Modulation (PWM) and Hysteresis Current Control (HCC) with PI controller simulated in MATLAB for different cases and percentage THD calculated to prove the effectiveness of the proposed method for the control of reactive power and THD with grid connected DSTATCOM. The results presented here justify that the HCC controller can be better than the PWM method to generate the PWM pulses for reduction of harmonics under various conditions of DTSTACOM to compensate the reactive power. Additionally, the simulation performed to check the efficacy of the projected method to reduce THD by varying the current control band of HCC.