Maximum power extraction from wind energy system using homotopy singular perturbation and fast terminal sliding mode method

In this paper, two strategies are proposed to simplify the dynamics and design of the controller for a variable speed wind turbine (VSWT) with a fractional order doubly fed induction generator (DFIG) in region 2. In the first strategy, the homotopy singular perturbation method (HSPM) is presented using fractional order singular perturbation method (SPM) and modified homotopy perturbation method (HPM). By exerting this method, the fractional order DFIG based VSWT is divided into two lower order subsystems, including nonlinear integer order subsystem and linear fractional order subsystem. In the second strategy, a nonlinear optimal second order fast terminal sliding mode controller (SOFTSMC) using the Lyapunov-based approach with negative definite solution is designed for nonlinear integer order subsystem. Also, a fractional optimal SOFTSMC is proposed by defining the subsystem error dynamics for linear fractional order subsystem. Finally, the control inputs designed for these subsystems are combined and applied to the original system. The main advantage of the HSPM is that both the integer and fractional modelings are used in the design process. The resulting fractional and nonlinear optimal SOFTSMC can be used effectively to achieve the maximum power extraction from the wind, reduce mechanical loads, attenuate the chattering, finite time convergence by applying a small control input, minimize the control input, ensure the better tracking, and tackle the effects of parametric uncertainties, unmodeled dynamics, and external disturbances. Stability of the original system is evaluated by investigating the Lyapunov stability theorem for each subsystem. The proposed controller designed by the HSPM is compared to some existing control laws, and their performance evaluation are reported in Table 1. The results of Table 1 guarantee the effectiveness of the proposed approaches.