In order to fully study the electrical, mechanical, and aerodynamic aspects of a wind turbine with a doubly fed induction generator, a detailed model that,considers all these aspects must be used. A drawback of many works in the area of wind turbine simulation is that either a very simple mechanical model is used with a detailed electrical model, or vice versa. Hence, the effects of interactions between electrical and mechanical components are not accurately taken into account. In this paper, three simulation programs - TurbSim, FAST, and Simulink - are used to model the wind, mechanical and electrical parts of a wind turbine, and its controllers. Simulation results obtained from the model are used to observe the interaction of all three factors affecting the operation of a wind turbine system. For example, it is shown how an electrical disturbance can cause dangerous tower vibrations under high speed and turbulent wind conditions, which may not be feasible using a simple model of the wind and wind turbine.