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Summary Accurate wind‐speed measure along with an effective control technology is an important aspect to attain optimal wind power. This paper proposes a sensorless maximum power point tracking (MPPT) algorithm that estimates the effective wind speed without an anemometer to reduce wind‐turbine installation cost and improve the overall efficiency. This algorithm depends on the aerodynamic torque power coefficient approximation to the third‐order polynomial. This paper investigates different control schemes of a 1.5‐MW grid‐tied five‐phase permanent magnet synchronous generator (PMSG) based, a variable‐speed wind‐energy conversion system (VS‐WECS). To eradicate the limitations of the proportional‐integral (PI) controller as a speed controller, model predictive controller (MPC) is implemented as a replacement of PI controller. The MPC is employed to track the rotor speed to the optimal speed. Both the PI and the MPC are designed and deliberated to satisfy the obedient performance of the speed control loop. Moreover, a comparative study of speed control schemes is performed between the conventional PI controller and the MPC. Performance of the proposed control schemes is validated using the MATLAB/SIMULINK. Simulation results show the superiority of MPC compared with the conventional PI controller and the validity of the MPC as a vital solution for drawbacks of the PI controller.