This paper proposes an optimal power management strategy for the islanded operation of smart transformer (ST)-based meshed hybrid low voltage (LV) microgrid. The main objective is to ensure that the line losses in the system are minimum. Accordingly, the power management scheme decides the reference powers for the storage systems and distributed generation (DG) converters during islanded operation. This ensures that the system has the maximum possible operation time with the available DG sources, battery energy storage systems and electric vehicles (EV). In case of surplus power generation, EVs are utilized for storage. This ensures that minimum DG power has to be curtailed, leading to maximum utilization of DG resources. The optimal power management problem is solved using genetic algorithm in MATLAB. Further, the proposed optimal power management strategy is verified through PSCAD simulations on the considered system of islanded ST based meshed hybrid LV grid.