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Wind energy is an environmentally friendly renewable resource, widely regarded as one of the most effective means to achieve sustainable development goals. A large number of variable-speed wind turbines (WT) around the world utilize double fed induction generators (DFIG). In the typical configuration of these systems, the stator is connected directly to the grid, while the wound rotor is powered via a bidirectional converter. This DFIG-WT configuration is effective for converting wind power due to several advantages: it operates at various speeds while keeping the stator frequency synchronized with the grid, supports both sub-synchronous and super-synchronous operating modes, and features a power converter that is minimized on the rotor side. Controlling such system presents a challenging engineering problem due to their nonlinear and interconnected dynamic models. The DFIG-WT must operate under severe operating conditions such as stochastic wind variations and parametric changes. Numerous robust controllers have been developed for DFIG-WT, focusing on achieving asymptotic stability in closed-loop control systems to ensure tracking error convergence over infinite time. Ensuring finite-time error convergence is essential in practice. This paper introduces a new adaptive neural network finite-time control approach for a variable-speed DFIG-WT. The main control objective is power extraction maximization while enhancing the wind energy system performance regarding convergence rate, tracking precision, and robustness to uncertainties. The proposed control approach utilizes adaptive neural network systems to handle system uncertainties effectively. The closed-loop control system finite-time stability is thoroughly confirmed and established through rigorous verification using the concept of finite-time Lyapunov stability of nonlinear systems. The effectiveness of the suggested controller is validated in numerical simulation using the Matlab/Simulink software. [ABSTRACT FROM AUTHOR]