Abstract — This paper presents a comparison between proportional integral **control** approaches for variable speed **wind** turbines. **Integer** and **fractional**-**order** controllers are designed using linearized **wind** **turbine** **model** whilst **fuzzy** controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the **wind** **turbine** while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of **fractional**-**order** proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral **fractional**-**order**, taking advantage over **integer** **order** proportional integral (PI) controller. A comparison between proposed **control** approaches for the variable speed **wind** turbines is presented using a **wind** **turbine** **benchmark** **model** in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and **fuzzy** PI controller outperforms the **integer** and **fractional**- **order** **control** due to its capability to deal with system nonlinearities and uncertainties.

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This paper investigates the operation of a hybrid power system through a novel **fuzzy** **control** scheme. The hybrid power system employs various autonomous generation systems like **wind** **turbine**, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel **fractional** **order** (FO) **fuzzy** **control** scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO **fuzzy** controller shows better performance over the classical PID, and the **integer** **order** **fuzzy** PID controller in both linear and nonlinear operating regimes. The FO **fuzzy** controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants.

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A variable **wind** **turbine** (WT) generates power in subrated and rated power regions. In the subrated region Fig.2. region II , the maximum achievable **turbine** power is a function of the **turbine** speed at any velocity. The maximum power tracking algorithms developed in the recent are **model** dependent. They have the drawback that the controller needs to be redesigned for each wecs. A similar system is presented in [1] where **fuzzy** **control** is used. It works only for the specified **fuzzy** rules. Another method based on the speed sensorless power signal feedback (PSF) [2] uses lookup table values that are dependent on the system **model** and parameter values. There is another method of perturb and observe (P&O) [3] is more accurate but slow convergence. To overcome these difficulties, we present **fractional** **order** extremum seeking (FOES) algorithm which is non **model** based and with easily tunable design parameters. The FOESC has many advantages over ESC.A system with ESC is shown in [4] which shows slow convergence. The convergence speed is faster in FOESC hence transient response is improved.

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However, there are essential differences between ordi- nary differential equation systems and **fractional** **order** differential systems. Most properties and conclusions of ordinary differential equation systems cannot be extend- ed to that of the **fractional** **order** differential systems. Therefore, the **fractional** **order** systems have been paid more attention. Recently, many investigations were de- voted to the chaotic dynamics and chaotic **control** of **fractional** **order** systems [6-12].

This paper explains about the different types of set-point controls for variable-speed **wind** generators. Both pitch angle **control** (PAC) and Rotor speed **control** (RSC) having their own advantages and disadvantages. Compared to PAC, RSC have better inertial effect which leads to better tracking in set-point command. Below set-point management this proposed paper illustrates the controllability of **wind** kind. However, the sturdiness of inertia impact mainly depends on the allowable rotor speed vary. The projected **wind** farm models not only ready to portray the set-point management underneath variable **wind** speed, this gives best solution by reducing the calculation burden which is useful for system analysis. Here we are using the **fuzzy** controller compared to other controllers. The different characteristics of **wind** farm and performance are shown in simulation results.

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E (α) ( t ) : = N 1 E ( X 2 (α) ( t )) , and I (α) ( t ) : = N 1 E ( X 3 (α) ( t )) , where N is the total population size and E ( x ) is the expected value of x. Thus using equation (11), and approximating E ( X 1 (α) ( t ) X (α) 3 ( t )) by E ( X 1 (α) ( t )) E ( X 3 (α) ( t )) we reach the **fractional** **order** version of the system of equations that was used by M . S . Bartlett [9] to **model** measles,

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Vortex-Bladeless is a Spanish SME whose objective is to develop a new concept of winturbine without blades called Vortex or vorticity **wind** **turbine**. This design represents a new paradigm in **wind** energy and aims to eliminate or reduce many of the existing problems in conventional generators. Due to the significant difference in the project concept, its scope is different from conventional **wind** turbines. It is particularly suitable for offshore configuration and it could be exploited in **wind** farms and in environments usually closed to existing ones due to the presence of high intensity winds. The device is composed of a single structural component, and given its morphological simplicity, its manufacturing, transport, storage and installation has advantages. The new **wind** **turbine** design has no bearings, gears, etcetera, so the maintenance requirements could be drastically reduced and their lifespan is expected to be higher than traditional turbines. It is clear that the proposed device is of prime interest, and that scientific investigation of the response of this **wind** energy generator under different operation scenarios is highly desirable. Thus, the objective of this SHAPE project is to develop the needed tools to simulate Fluid-Structure Interaction (FSI) problems and to reproduce the experimental results for scaled models of the Vortex- Bladeless device. In **order** to do so the Alya code, developed at the Barcelona Supercomputing Center, is adapted to perform the Fluid-Structure Interaction (FSI) problem simulation.

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It should be pointed out that in the above mentioned literature, synchronization of **fractional**-**order** or **integer**-**order** chaotic systems was mainly discussed. Synchronization between **fractional**-**order** and **integer**-**order** chaotic systems is widely perceived as con- tributing to generating hybrid chaotic transient signals, which are quite diﬃcult to be de- crypted in communication. Up to now, only a few works have been given to investigate this problem, for instance, by using the stability theory of **fractional**-**order** linear system, Ref. [] investigated modiﬁed general functional projective synchronization between a class of **integer**-**order** and **fractional**-**order** chaotic systems. Ref. [] discussed the dual projective synchronization between **integer**-**order** and **fractional**-**order** chaotic systems (one can refer to [–] for more details). Actually, some dynamical systems usually have non-identical dimensions. However, papers which have discussed the synchroniza- tion between **fractional**-**order** and **integer**-**order** chaotic (hyper-chaotic) systems with dif- ferent dimensions are not common. Ref. [] investigated adaptive generalized function matrix projective lag synchronization between **fractional**-**order** and **integer**-**order** com- plex networks with delayed coupling and diﬀerent dimensions. However, the controller in [] has a very complicated form. Note that two scaling matrices (a function matrix and a non-unit constant matrix), which are more general than other scaling factors in FPS, have not been used to discuss the synchronization between **fractional**-**order** and **integer**-**order** chaotic (hyper-chaotic) systems with diﬀerent dimensions. Besides, it is well known that the quadratic Lyapunov functions provide an important tool for stability analysis in the **integer**-**order** nonlinear systems. Therefore, how to use quadratic Lyapunov functions in the stability analysis of **fractional**-**order** systems is meaningful.

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Abstract: In this paper, **Fuzzy** Logic **Control** (FLC) and Predictive Torque **Control** (PTC) methods are being introduced separately at grid side converter (GSC) of Doubly Fed Induction Generator (DFIG) based **wind** **turbine**. There are two parameters usually challenging for the power rating of a **wind** energy conversion system (WECS): improper **control** strategy for RSC, which is the primary reason behind current harmonics and for GSC, it is the reason behind voltage harmonics. In several **wind** **turbine** systems while maintaining these harmonics leads to improper electromagnetic torque. This two fold effect of controller is worst while using same controller for both GSC and RSC. Firstly, in this improved controller architecture, the general structure of conventional controller is retained and **Fuzzy** Logic is used to provide intelligence to the operation of controller. In several research works it has been seen different controllers for both side, resulting improved results. Secondly, a predictive methodology has been adopted which predicts torque and stator current to be used as reference signal in controlling GSC and a well-tuned PI controller for RSC. The results are being compared that shows significant reduction in harmonics at rotor side and grid side.

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This paper focuses on analyzing the output behavior of **wind** turbines with DFIG when using **fractional**-**order** **control** system and improves the power quality and power and voltage stability in comparison with using classic **control** system during **wind** variations, considering two types of ac/dc/ac power electronic converters. Also, modeling, **control** and simulation of **wind** **turbine** with PMSG using **fractional**-**order** **control** system can be found in [9]. The simulation results are shown in the last sections by using MATLAB/Simulink. A better operation can be seen when utilizing **fractional**- **order** **control** strategy.

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In this work, an intelligent artificial **control** of a variable speed **wind** **turbine** (PMSG) is proposed. First, a mathematical **model** of **turbine** written at variable speed is established to investigate si- mulations results. In **order** to optimize energy production from **wind**, a pitch angle and DC bus **control** law is synthesized using PI controllers. Then, an intelligent artificial **control** such as **fuzzy** logic and artificial neural network **control** is applied. Its simulated performances are then com- pared to those of a classical PI controller. Results obtained in MATLAB/Simulink environment show that the **fuzzy** and the neuro **control** is more robust and has superior dynamic performance and hence is found to be a suitable replacement of the conventional PI controller for the high per- formance drive applications.

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The characteristic of **wind** velocity is fluctuant. The value of **wind** velocity at a fixed height fluctuates around a certain value, which is called static **wind** velocity. The random fluctuation value of **wind** velocity is called fluctuating **wind** velocity. Take horizontal component of **wind** velocity (horizontal **wind** velocity) as an example, its formula is shown in as follows.

speed, does not have rotor current, and can be used without gearbox. The high efficiency and low maintenance will reduce the cost that is the most concern to invest. However, PMSG still has some drawbacks. It needs electromagnetic field with the flexible structure, which leads to the high standard of the production as well as of the operation. Furthermore, variable speed of the generator has to be known by power inverter too. According to the continuous development of **wind** power technology, the efficiency of inverter device, facing some tough issues, plays an important role in the improvement of **wind** power generation system performance. They need to be enhanced by novel controller [3] to improve the efficiency and the reliability. Inside them, MPPT integrating with the back to back space vector PWM [4] is the advantage **control** novel in [3], which is used to measure the rotor speed and compare with the calculated optimal rotor speed. On the other hand, not only does the inverter take an advantage in efficiency **control** but also the pitch angle controller takes another important part of **wind** **turbine**. It is integrated to adjust the aerodynamic torque of the **wind** **turbine** when this study rates **wind** speed.

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Stability analysis of nonlinear systems is necessary to design a controller. Several works have investigated stability analysis of nonlinear systems by means of **fractional** calculus [26-30]. In [26], **fractional** generalization of concept of stability was considered. In [27], a definition for Mittag-Leffler stability and **fractional** Lyapunov direct method were presented. In [28], stability analysis of FO nonlinear systems was derived using the Lyapunov direct method with Mittag-Leffler stability. In [29], stability of **fractional** differential systems based on the conformable **fractional** derivatives was studied. However, there are very few papers considering modelling of the nonlinear systems with conformal FO definition [29,30]. Therefore, **application** of the conformable FO operators in the design of FO controller is an open area. Accordingly, for the first time, in this paper, a FO sliding mode **control** is designed for a class of conformable **fractional** **order** chaotic system using the conformable **fractional** derivative and the superiority of the proposed controller is shown. Having these facts in mind, the main contributions of this paper in comparison with previous researches are as follows. A novel FO manifold using conformable FO operators is proposed to **control** chaotic systems in the presence of uncertainties and disturbances. The conformable FO operator as an interesting definition is applied in designing of the FO sliding mode controller. Based on conformable FO operators, the stability of the controller is derived using the Lyapunov direct method. The main advantage of the proposed **control** method is fast convergence speed with together less chattering and complexity in calculations.

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The concept of **fuzzy** derivative was ﬁrst introduced by Chang and Zadeh [1]. Kaleva [2], Puri and Ralescu [3] introduced the notion of **fuzzy** derivative as an extension of the Hukuhara derivative and the **fuzzy** integral, which was the same as that proposed by Dubois and Prade [4]. There has been a signiﬁcant development in the study of **fuzzy** dif- ferential and integral equations (see, for example, [5–8], and the references therein). Under suitable conditions, it was proved in [9] that the boundedness of solutions of the following **fuzzy** integral equation:

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In recent years renewable sources of power are being increasingly exploited to address the challenges of climate change and fossil fuel depletion. **Wind** power is one of the few renewable energy sources capable of rapidly satisfying a reasonable proportion of future energy requirements. **Wind** turbines will be expected to significantly increase the power outputs with an improved efficiency and reliability. The advantages of **wind** energy are more apparent than the disadvantages. Next, harvesting **wind** power is a clean, non-polluting way to generate electricity. Unlike other types of power plants, it emits no air pollutants or greenhouse gases. The **wind** turbines harmlessly generate electricity from **wind** passing by. Since the population of India keeps on increasing, the implementation of **wind** turbines with most profitable power production is needed to satisfy the future power needs. **Wind** energy, with an average growth rate of 30%, is the fastest growing source o f r e n e w a b l e energy in the world. India occupies the fifth place in the w o r l d i n **wind** energy generation after USA, Germany, Spain, and China. Since t h e maximum speed of **wind** blade is from 55 mph to 161 mph, it is necessary to

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For the high **wind** speed zone, the desired operation of the **wind** **turbine** is to keep the rotor speed and the generator power at constant values. The main idea is to use the pitch system to **control** the efficiency of the aerodynamics while applying the rated generator torque. However, in **order** to improve tracking of the power reference and cancel steady state errors on the output power, a power controller is usually considered as well [3, 8, 9]. Hence, both speed **control** and power **control** are included in practice.

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There are many aspects of **wind** **turbine** performance that can be improved with more advanced **control** development. Researchers have developed methods for using adaptive **control** to compensate for unknown or time–varying parameters [15]. Other researchers have also begun to investigate the addition of feed-forward **control** to improve the disturbance rejection performance when the incoming **wind** profile deviates from that expected [16]. Most of these feed-forward controllers use estimates of the disturbance (or **wind** deviation). New sensing technologies will enable various avenues of advanced **control** research. For instance, there has been recent interest in evaluating the potential of LIDAR (which stands for “LIght Detection And Ranging”) sensors for **wind** **turbine** **control** [16]. LIDAR is a remote optical sensing technology that has been used since the 1970s for meteorology for measuring **wind** speed profiles for monitoring hurricanes and **wind** conditions around airports. New lidar systems based on solid–state sources and off–the–shelf telecommunications equipment allow for inexpensive deployment, modularity, and improved reliability. Depending on the particular type of technology used, lidar sensors can provide quantities representing the **wind** speed and direction and various **wind** turbulence and shear parameters. An accurate measurement of the **wind** profile over the entire rotor plane in Fig. 7 can enable feed-forward pitch **control** and feed-forward torque **control** to improve performance dramatically. Advanced **wind** **turbine** controllers are further discussed and compared in [4, 16]. As turbines get larger and blades get longer, it is possible that **turbine** manufacturers will build turbines that allow for different pitch angles at different radial positions along the blades relative to the standard blade twist angle. In this case, separate actuators and controllers may be necessary, opening up even more **control** opportunities [16].

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The continuous **model** reported in Section 2 includes various modules and dynamics, including aerodynamics module, rotor dynamics module and drive-train module. The drive-train module is stiff and linear. Stiff systems have poles of very different magnitudes, i.e. some poles close to the origin (in the s-plane) and some poles very far away from them, meaning that they contain both slow and fast dynamics. This therefore makes it difficult for the numerical integration solver of Matlab/SIMULNIK to choose a correct and optimal sampling step when simulating the stiff drive-train module, and the solver thus has a strong tendency to opt for a very small sampling step, as opposed to a larger optimal sampling step, resulting in a significant increase in simulation time. This is avoided here by optimally discretising the stiff drive-train module in advance and thereby not requiring numerical integration to be carried out at all during simulation.

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These conditions are met by a variable speed windmill with fixed blade pitch driving a self excited induction generator, the electrical power being fed into the heating elements through [r]

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