A multifrequency microgrid (MFMG), which has different frequency voltages and currents on the multifrequency (MF) bus can be constructed based on superposition theorem, orthogonal power flow theory, and frequency selective power transmission criteria. It is a unique system where different frequency powers are present on the bus and all active powers maintain orthogonality by flowing simultaneously through a conductor without mixing. Due to the uncertainty and intermittency of renewable sources, an energy storage system (ESS) needs to be installed with MFMG to maintain stability and reliability. The ESS will be charged/discharged based on different frequency active power imbalances in the MF bus. Due to the presence of different frequency voltages and currents on the MF bus, the integration of ESS with MFMG is challenging but not yet discussed in any literature. In this paper, an architecture of MFMG is proposed with ESS. It is found that different new power imbalance cases arise in MFMG due to different frequency sources and loads, which are not present in traditional microgrids. Here, active power balancing conditions for all power imbalance cases are defined for grid connected and islanded mode. An algorithm is proposed to coordinate the ESS and different renewable sources to balance different frequency active power demands in MFMG for optimum power generation through communication under a cooperative framework. The framework is created based on the assumption that any load prefers to take power from the nearest source to minimize the power loss and cost. Different source load pairs are categorized based on the physical distance by different frequencies and accordingly the algorithm is structured. Finally, Matlab simulation of a sample 9 bus MFMG is performed to validate the algorithm and all results are presented.