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In this article, an adaptive normalized Sign Regression Least Mean Mixed Norm (ε-NSRLMMN) algorithm-based control technique is developed for the Shunt Active Power Filter (SAPF) to compensate for the grid current harmonics and reactive power under balanced and unbalanced loading conditions. The adaptive ε-NSRLMMN control algorithm improves power quality and makes the source current sinusoidal and power factor (PF) close to unity. It is used for load compensation in a three-phase distribution network. The fundamental active component is extracted from the distorted load current using an adaptive technique. This control algorithm has the advantages of improved convergence, better stability, lower harmonic distortion, less complexity and less steady-state error than the Sign regressor least mean mixed norm (SRLMMN), Least mean square (LMS) and least mean fourth (LMF). Adaptive ε-NSRLMMN is used for learning the fundamental active weight components of the load current. The parameters of the proposed algorithm are trained in real-time. A traditional PI controller has been used to regulate the dc-link voltage of the Voltage Source Converter (VSC). The performance of the proposed algorithm has been justified by simulation and experimental results. [ABSTRACT FROM AUTHOR]