Economic nonlinear model predictive control (ENMPC) is a strong candidate for controlling wind turbines (WTs). In the model predictive control (MPC) group, the model is the crucial component for the true controller performance. It is common to use simplified models to reduce the problem complexity. These models neglect some of the underlying dynamic responses of real wind turbines. This paper simulates the case in which high accuracy nonlinear models describe both the plant and the controller. The results will be compared to reduced-order models in order to extract conclusions and decide the most appropriate model for WT control. On the other hand, one of the main features of MPC and ENMPC is the concept of receding prediction horizon, which considers the future evolution of the plant to compute the control action. The error of prediction will drastically reduce MPC performance. Also, rapid variation in wind speed can cause problems since wind turbines cannot easily follow these sudden variations due to their high inertia and aerodynamic characteristics. This paper provides an advanced control approach to improve the energy extraction from turbulent wind and enhance wind turbine durability. By implementing this method, the wind speed forecasting is done with a combination of artificial neural networks (ANN) and dynamic equations applied in ENMPC. The results show a significant enhancement of the control performance.