# Wind Turbines Optimal Operation at Time Variable Wind Speeds
## 1 Introduction  
Renewable energy has become a very important research area during the last few decades, and wind farms are a resource-efficient option for generating electric energy. The main drawback, though, is that the wind resources are affected by wind volatility, and furthermore, sudden wind speed variations lead to the unstable operation of the wind turbine [1]. As is highlighted in [2], from the energy point of view, the operation of the wind turbines within the optimal area was treated mainly for constant wind speeds over time. In reality, the wind speed is a time-varying function, and in order to operate within the optimal area from the energy point of view, the angular speed of the permanent magnet synchronous generator (PMSG) must follow the wind speed variation in time, because the PMSG's optimal angular speed is directly proportional to the wind speed value, as was shown in [3]. Tracking the maximum power point (MPP) is the essence of the variable speed wind turbines' control, since it determines their efficiency. The MPP is achieved by always adapting the wind turbine's speed to the wind speed [4]. There are five main categories of MPP tracking methods: power signal feedback (PSF) control [5], optimal torque (OT) control [6], tip-speed ratio (TSR) control [7] and perturbation and observation (P&O) control [8; 9]. There are also artificial intelligence techniques, such as fuzzy logic [10], artificial neural networks [11], intelligent search algorithms [12] and wind turbine power curves (WTPC) [13; 14; 15]. PSF- and OT-based MPP tracking methods employ the generator's exact model, commonly used in large-scale wind turbines [6; 7]. The torque is usually estimated using the Kalman filter [16]. Since the wind turbines can change their rotation speed to follow changes in wind speed, this means that for each wind speed there is an ideal rotational speed, which is called the optimal tip-speed ratio (TSR), and is different for each wind turbine [7]. Thus, the TSR-based MPP tracking method uses the wind turbine's exact model. The wind speed and the tip-speed ratio are estimated using the Newton-Raphson method. The error between the estimated torque and the steady optimal torque is used as the feed-forward signal to control the generator torque. Unfortunately, there is a conflict between the rapid wind variations and the slow dynamic response of the wind turbines, due to the large inertia of the generator. Regarding the P&O method, it was demonstrated in the literature that this fails to follow the MPP trajectory of the under rapid wind variations [8]. For high efficiency, instantaneous MPP is highly demanded, but this claims high controller robustness against parameter variations and external disturbances. Therefore, fuzzy and artificial intelligence-based MPP tracking methods represent a flexible medium, that proposes solutions to problems that cannot be tackled with traditional methods. Many papers have stated that the sliding mode control approach is more robust with respect to parameter variations and external disturbances [17]. Nevertheless, chattering is its main drawback. To address this, higher order sliding mode control was developed [18]. Due to the uncertain nature of the wind, in order to make wind energy a reliable source, accurate models for predicting the delivered power and performance monitoring of wind turbines are needed. The wind turbine's power curve, which gives the turbine's delivered power at a specific wind speed, provides a convenient way to model the performance of wind turbines. A number of methods have been proposed in the literature for WTPC modelling, as follows: parametric models, parameter estimation, data preprocessing, evaluation of model, and nonparametric models (i.e., the artificial neural networks method and the fuzzy logic method, this one being used when the data collected from the wind farms is voluminous, and usually contains errors). They have their own advantages and disadvantages.