This paper introduces a novel approach to enhance power quality in distribution networks connected to lowvoltage AC-DC residential-industrial microgrids. The proposed method leverages a Distribution Static Synchronous Compensator (DSTATCOM) utilizing improved three-level coupled-inductor Z-source inverters (ZSIs). A comprehensive static and dynamic analysis is first conducted on classical Γ-ZSI, Y-ZSI, and trans-quasi-ZSI (TQZSI) models, leading to the development of three improved designs. These designs are tailored to enhance power quality by reducing harmonic pollution at the grid connection point, increasing power factor, improving stability, mitigating voltage unbalance, and minimizing control complexity and structural costs. Additionally, the proposed method incorporates an analysis of the battery lifespan on the DC source side of the DSTATCOM. The DSTATCOM models are simulated in a distribution system connected to a real-world AC-DC residential-industrial microgrid through software implementation. The results across various scenarios demonstrate the effectiveness of the proposed design, highlighting its capability to achieve desirable power quality improvements.