This paper focuses on improving the low voltage ride-through (LVRT) capability of grid-integrated AC-Microgrid (AC-MG) during grid faults. Enhancing LVRT ensures grid connectivity during faults and helps meet grid code requirements. The paper explores LVRT improvement topologies for the renewable-integrated AC-MG, discussing their advantages and disadvantages in reducing over-voltages and voltage fluctuations in the grid. To augment the transient stability of the AC-MG, a new hybrid algorithm approach, the least mean-square (LMS) and the maximum Versoria criterion (MVC)-based adaptive algorithm, is proposed in this paper for the voltage source converter (VSC)-STATCOM and VSC of the superconducting magnetic energy storage (SMES) device. The MVC algorithm augments the transient stability of the grid-coupled AC-MG by dynamically adjusting both the PI controllers of the VSC and the dc-dc chopper in the SMES system and VSC-STATCOM through rapid convergence velocity. A practical 1 MVAR STATCOM and 0.78 MW SMES system is connected at the PCC of AC-MG. The validation of the proposed MVC-PI controllers for the STATCOM and SMES systems is compared with the least mean square (LMS)-based PI controllers under grid disturbances. The proposed control topology is implemented using MATLAB/Simulink software. The power quality of AC-MG can be further augmented by the controlled SMES and STATCOM systems.