Battery energy storage systems (BESS) have been integrated with wind turbines to mitigate wind intermittence and make wind power dispatchable as traditional power sources. This paper presents a new power dispatch and control methodology that allows an integrated wind turbine and BESS to provide the grid with consistent and optimal power within a predetermined dispatch interval. First, the desired battery state of charge (SOC) under each wind speed is determined by applying an offline probabilistic algorithm to historical wind speed and power data. With this information, a one-step ahead model predictive optimization approach is explored for scheduling the integrated system power output for the next dispatch interval. Then, a real-time controller is developed to make the actual system power output match the scheduled target. A wind turbine active power controller is proposed to track the reference power set point determined by a steady state optimization approach. By combining an internal integral torque control and a gain-scheduled pitch control, the proposed active power controller can operate in a desired rotor speed region without an accurate knowledge of wind turbine operating parameters. Compared to the conventional scheduling approaches and real-time controller, implementing the new methodology significantly reduces the ramp rate, generator torque changing rate, battery charging rate and the power output deviation from the scheduled target. BESS with various capacities and different wind profiles are considered to demonstrate the effectiveness of the proposed algorithms on battery sizing.