Recently, the establishment of technical standards for grid connection has gained interest in academia and industry. These standards have focused on the reactive power control function of the grid-connected inverter and maintenance of grid operation, and include detailed information about the grid support function. However, remote control communication and control devices for grid support functions, and other distributed sources, such as wind power and energy storage systems, other than inverters have not been addressed. In this paper, the control of the interlinking converter (ILC) in a hybrid microgrid considering low voltage ride-through (LVRT) among grid support functions is investigated. The proposed method consists of an energy management system considering LVRT and a cooperative control scheme. In the energy management system, an algorithm capable of mode selection was constructed by applying the LVRT curve. Then, considering the LVRT situation, the allowable reactive power range of the ILC was mathematically analyzed through the cooperative control of the energy storage device and the ILC. The proposed method enables us to perform active and reactive power control of the ILC in a hybrid distribution network, considering the power factor under various conditions. This functionality, such as supplying reactive power, significantly contributes to the enhanced grid resilience with distributed power sources, including renewable energy. The proposed strategies were verified through experiments after configuring an experimental set of distributed power sources.