Microgrids are being evolved as a potential alternative to reduce unrelenting dependency on central utility grids. Moreover, integrated multi-microgrid based clusters are forming in closed vicinities to enhance the benefits of microgrids. However, the power quality problem is one of the key issues to be solved in such systems, which is mainly caused by the rising penetration of nonlinear loads and interfacing of power electronic converters. To address this issue, this paper proposes a new control technique, named "adaptive neuro-fuzzy control strategy". This controls the inverter of each microgrid in the cluster as well as the voltage source converter based distribution static compensator located at the point of common coupling between the cluster and the utility grid. This proposed control strategy uses the advantages of both fuzzy logic and artificial neural networks, thereby effectively controls the system. The proposed technique is modelled in MATLAB/Simulink software 2021a. For the analysis, various power quality indices such as voltage sag/swell, voltage unbalance, frequency deviations, power characteristics, total harmonic distortion, and neutral current compensation are measured. These indices of the proposed controller are compared with conventional PI and fuzzy logic-based controllers in view of various key IEEE/IEC standard tolerances. From these results, the proposed controller has proved its superiority. postdoctoral fellow. He has authored/co-authored more than 60 research articles. His research interests include microgrids, electric vehicle, charging infrastructure, grid integration, energy management systems, etc.