This paper presents the shunt compensation performance of quasi- Z-source inverter (QZSI) and back to back connected QZSIs (BB-QZSI) to addressed the power quality (PQ) issues in the three phase three wire power utility network (PUN). Generally, these PQ issues are poor voltage regulation, low power factor, source current distortion, and unbalanced voltage etc. The proposed BB-QZSI based distribution static compensator (DSTATCOM) consists of two QZSIs with a common DC link capacitor. Because the QZSI could achieve buck/boost conversion as well as dc to ac inversion in a single-stage and the back to back configuration decreases the system down time cost (if fault occurs in one QZSI the other can continue the shunt compensation). Particularly, icosϕ control algorithm is implemented to generate proper switching pulses for the switches of DSTATCOM. The effectiveness of the BB-QZSI is verified through simulation studies over QZSI using MATLAB/Simulink software satisfying the recommended grid code.