A wind turbine system with an new open-end-winding permanent magnet synchronous generator (OEW-PMSG) is studied in this paper, with a focus on torque ripple minimisation of the OEW-PMSG. The problem of torque ripple minimisation of OEW-PMSGs is addressed. Generally, the q-axis current injection method is employed to suppress the torque ripple. However, the third flux linkage parameters will be affected by high temperature when the machine is operating. In order to solve this problem, two sensorless adaptive control methods are presented in the following paper. The first method is based on adaptive sliding mode control and deadbeat-based predictive current control. The second method is based on model reference adaptive control with deadbeat predictive control. In these two control systems, a zero-sequence back-EMF observer (ZCBO) is used to estimate the zero-sequence back-EMF and zero-sequence current simultaneously and continuously. Meanwhile, the zero-sequence voltage which exists in the zero-sequence path and interferes the ZCBO's performance is considered. The performance of two control strategies is evaluated in MATLAB/SIMULINK environment.