A dynamic model for simulating behavior of a horizontal axis wind turbine (HAWT) with differential planetary gearbox is developed. The aerodynamic load applied to the wind turbine connected with the carrier is described using the quasi-steady approach. The control torque is assumed to be applied to the external ring of the gearbox. Steady regimes of the device are analyzed, and their stability is studied. For the case of constant control torque, power costs are estimated required for preserving constant angular speed of the generator.