Two novel approaches to capture the maximum power from variable speed wind turbines using optimal fractional high-order fast terminal sliding mode control

Abstract

In this paper, two nonlinear control approaches using optimal fractional high-order fast terminal sliding mode (FHOFTSM) control are proposed to maximize the captured wind energy and minimize the mechanical loads in the variable speed wind turbines (VSWTs). The optimal condition of the system which uses the presented approaches is achieved by creating a compromise between maximizing the energy extraction and minimizing the control input. So, the mechanical stress on the drive-train is reduced by minimizing the control input. To achieve this compromise, the behavior of the wind turbine system should be precisely modeled. Fractional calculus theory is an effective method for modeling the VSWT, which provides a more accurate description of the system performance compared with integer-order modeling. Based on the fractional-order modeling of the system, the optimal approach is designed by calculating the error dynamics of the system and defining two types of performance indexes, integer-order and fractional-order performance indexes. Hence, the design procedure of an optimal FHOFTSM control for each performance index requires two-stages process. At first phase, an optimal controller is presented for the system nominal error to minimize the quadratic performance index. Then a switching controller is offered in the second phase that is obtained by defining the fractional high-order sliding manifold and fractional nonsingular fast terminal sliding manifold to overcome the unknown disturbance. Hence, the order of the controllers is smaller than the second order. The optimal strategy is applied to minimize the control input, whereas the FHOFTSM method is used to obtain the maximum wind power extraction, reduce mechanical loads, attenuate the chattering, and achieve fast finite-time convergence. The closed-loop stability of the control system is approved by the fractional Lyapunov direct method and the Mittag-Leffler stability theorem. To illustrate the effectiveness of the proposed approaches, the proposed controllers are compared with some already existing controllers. The performance of controllers is verified through three scenarios, i.e., random variation of wind speed, step change of wind speed, and robustness against parameter uncertainties, in which the simulation results confirm the effectiveness of the proposed controllers.