A supervisory hybrid control design approach is proposed for the operation and control of a wind energy conversion and battery storage system during grid-connected and in islanded operation. A finite hybrid-automata based modeling paradigm for the system is presented. The proposed model defines the allowable operating states and inter-state transition paths managed by the supervisory control layer. The subject system has been partitioned into three independent system modules using a modular control design approach. The supervisory control layer combines and configures control schemes of the constituent modules to suite the requirements of operation during any one operating state of the system. Transition management strategies implemented through the supervisory control layer ensure smooth inter-state transitions and bumpless switching among regulators. Detailed mathematical models of the system are provided in each operating state. Frequency domain linear analysis and time domain electromagnetic transient simulations are presented for the microgrid system under steady state and dynamic operating conditions including temporary faults on the utility grid.