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In this paper, a type of variable step size LMS named weighted zero attracting variable step size (WZAVSSLMS) is equipped with the control algorithm for governing DSTATCOM. In WZAVSSLMS, the ability of zero attracting nature to a variable step size (VSSLMS) for improving convergence rate is observed. WZAVSSLMS algorithm-based fundamental extractor is developed to identify the fundamental quantity of the load current for a three-phase four-wire DSTATCOM with non-linear load in this work. This type of variable step size LMS has provided a concession for quick convergence rate and steady-state error. Precision and convergence of responses are accomplished by the learning rate control. As a result of these features over conventional LMS, the authors choose WZAVSSLMS based approach in well-known DSTATCOM system to compensate power quality issues. The fundamental extraction from the distorted load current constitutes the main divergences in the proposed study. Further, the Finite control set model predictive control (FCS MPC) of the distribution static compensator (DSTATCOM) using Weighted Aggregated Sum Product Assessment Solution (WASPAS) method is implemented. [ABSTRACT FROM AUTHOR]