Optimal power tracking of PMSG based wind energy conversion systems by constrained direct control with fast convergence rates

•Simplicity: No aerodynamic torque, wind speed or current sensors required, reduced online computation by using deadbeat inputs.•Effectiveness: Optimal power tracking, fast dynamics, reduced switching frequency with more balanced among legs.•New Techinques: Sum-of-Square Observer Design, Stability for Direct Control. This paper proposes a simple direct control with fast convergence rates under constraints for tracking optimal power of permanent magnet synchronous generator (PMSG) based wind energy conversion system (WECS). The simplicity features are on neglecting the following: predicted control performances, measurement of aerodynamic torque/wind speed and stator currents. The superior features are on very fast and accurate tracking performances with asymptotic convergence and well-regulated stator currents. First, a nonlinear observer is designed to observe both aerodynamic torque and stator currents. The wind speed is then inferred from the estimated aerodynamic torque and consequently, the optimal speed reference is identified. Next, the conditions of asymptotic stability for the closed-loop dynamics are formulated. Finally, a simple direct control is proposed to maximize the convergence rates in transient states and reduce switching frequency in steady states. Comparative studies with finite set model predictive control are presented to validate the advantageous features of the proposed method. The comparative results show that the superiority of the proposed method is proved by better controlled outputs with lower ripples, smaller steady-state tracking errors, faster response in transient-states, good tracking performance even for fast-varying aerodynamic torque, and lower average switching-frequency.