With the increasing proliferation of high-tech loads and electrical vehicle (EV) charging stations, shunt active power filters (SAPFs) are contemplated to play a growingly substantial role in power distribution and delivery. In this regard, this paper proposes a Lyapunov based harmonic compensation and charging with the operation of three-phase SAPF as interface EV applications and the electric grid. The proposed control algorithm provides effective harmonics mitigation capability under various non-linear loads (NLLs) groups and grid disturbances. A noteworthy contribution of this paper is that a Lyapunov based proportional integral with anti-windup (PI with AW) control is proposed to regulate oscillations of the DC-link voltage without increasing DC-link capacitor size. The proposed control algorithm offers comprehensive solutions with several improvements, novelties and features as: (i) keeping the total harmonic distortion (THD) of source currents below recommended IEEE-519 limits, (ii) extraction of reference current and voltage signals based on Lyapunov estimator (LE) with effective and good harmonic rejection capability, (iii) achieving good dynamic performance with utilizing a Lyapunov based PI with AW control for the DC-link capacitor voltage and (iv) eliminating the necessity of any high-pass or low-pass filters with utilizing LE based orthogonal signal generation (OSG). Besides, comparative analyses with previous studies are handled to examine improvements provided by the proposed control algorithm. The feasibility and effectiveness of the proposed control algorithm are confirmed by PSCAD/EMTDC environment and DSP based PIL quasi-real time results.