This paper focuses on the design and control of a new concept for wind turbines with a planetary gearbox to realize a power split. This concept, where the generated wind power is split into two parts, is to increase the utilization of the wind power and may be particularly suitable for large scale off-shore wind turbines. In order to reduce the cost of the power electronic devices, a synchronous generator, which is driven by the planetary gear, is directly connected to the power grid without electronic converter. A servo drive, which functions as the control actuator, is connected to the power grid by a power electronic converter. With small scale power electronic device, the current harmonics can also be reduced. The speed of the main shaft is controlled to track the optimal tip speed ratio. Meanwhile the speed of the synchronous generator is controlled to stay at the synchronous speed. The minimum rated power of the servo motor and the converter, is studied and discussed in this paper. Different variants of the wind turbine with a planetary gear are also compared. The controller for optimal tip speed ratio and synchronous speed tracking is given.