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This paper presents the shunt compensation performance of quasi-Z-source inverter (QZSI) and back to back connected QZSIs (BB-QZSI) to address 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 (PF), source current distortion, unbalanced voltage, etc. The proposed BBQZSI-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 a fault occurs in one QZSI the other can continue the shunt compensation). Particularly, icos ϕ control algorithmcontrol 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.