Doubly-fed induction generator (DFIG) wind turbine has been widely used in wind energy industry due to its good energy capture performance, fine controllability and simple realization. In this paper, a mathematical model for the operation and control of a DFIG wind turbine was proposed. Battery storage device with a PID controller was connected to the grid side aiming at obtain a smooth power output of wind turbine under different wind conditions. The present model was numerically solved under different wind conditions, i.e. a constant wind, a sinusoidal-type wind and a step-type wind. The simulation results showed that DFIG wind turbine with a battery storage device could provide a much smoother power output at different wind conditions comparing with the conventional DFIG wind turbine. Furthermore, compared to other models, our model has some advantages such as less cost, easily manufacturing and maintenance and therefore can be used in wind energy industry.