This article proposes a control architecture for a low-voltage AC microgrid with distributed battery energy storage. The droop controlled inverters interact with the microgrid through the RL combination of their virtual resistive output impedance with the series impedance of a coupling transformer. To obtain independent association of frequency with active power, and voltage with reactive power, decoupled droop control techniques are proposed and analyzed. The resulting control can be adjusted for appropriate dynamic response without modifying the droop coefficients. The application in the microgrid in diverse operating conditions is verified by a detailed simulation. The resulting primary control layer offers the capability of being easily actuated from a secondary control layer for procedures such as flexible power dispatching and frequency restoration.