The installation of an energy storage system (ESS) is vital for the Micrgorid (MG) islanded operation to ensure the maintenance of demand-supply balance. Lithium-ion batteries (LIBs) are among the most commonly used ESS technologies for grid-based applications, which is used in this paper to constantly maintain the demand-supply balance in a residential MG. For this purpose, a novel frequency-based energy management scheme is proposed. It uses an LIB ESS to handle the primary frequency control and energy management during peak-load period, while the dispatchable distributed generators like microturbine and fuel cell supply the base load. The air-conditioning TCLs consume a significant part of the residential load profile, especially during mid-summer. Unlike TCLs that instantaneously use their generated cooling thermal energy to control indoor temperatures, the thermal energy storage systems (TESSs) can also store the thermal energy and use it later. In this paper, the TESSs are used instead of TCLs to reduce the power consumption of a residential Microgrid (MG) in islanded mode. By doing this, the required LIBESSs capacity is decreased 70% considerably than the case the TCLs are used for controlling the indoor temperatures. Also, replacing the ACs and EHPs with TESSs results in a 63.7% reduction in the total cost of electrical and thermal storage.