In this study, a control strategy for energy storage elements (ESDs) which includes batteries and supercapacitors is proposed to enhance LVFRT under balanced and unbalanced faults. The MG comprises wind farms and/or photovoltaic arrays. Based on the dynamic simulations using MATLAB/SIMULINK, the ESDs can enhance LVFRT capability. A comparison of the conventional crowbar scheme and ESDs is realized, and the latter has a better performance than the former in retaining the DC-link voltage within satisfactory bounds. For the purpose of maintaining the DC-link voltage at a reference level, the battery stores extra power in the DC-bus of three systems. LVFRT is improved by the crowbar circuit, however the resistance consumes the extra power. Super capacitors (SCs) prevent DC voltage fluctuations, reduce active power oscillations, and hasten system stabilization when present. At an advanced stage of this effort, the coot bird optimizer (CBO) is applied to generate the best gains of bi-directional converter PI-controller and the ESDs ratings