MPPT control design for variable speed wind turbine

Variable speed wind turbine systems (VSWT’s) have been in receipt of extensive attention among the various renewable energy systems. The present paper focuses on fuzzy fractional order proportional-integral (FFOPI) control segment for variable speed wind turbine (VSWT) directly driving permanent magnet synchronous generator (PMSG). The main objective of this study is to reach maximum power point tracking (MPPT) through combination of advanced control based on FFOPI control applied to generator side converter (turbine and PMSG). The basic idea of the FFOPI controller is to implement a fuzzy logic controller (FLC) in cascade with Fractional Order Proportional Integral controller (FOPI). A comparative study with FOPI and classical PI control schemes is made. The traditional PI controller cannot deliver a sufficiently great performance for the VSWT. However, the results found that the proposed approach (FFOPI) is more effective and feasible for controlling the permanent magnet synchronous generator to mantain maximum power extraction. The validation of results has been performed through simulation using Matlab/Simulink®.


INTRODUCTION
An alternative energy source such as wind energy is more environmentally acceptable when compared to the traditional fossil fuels-based energy sources. Wind power depends mainly on geographic and climate conditions. For that reason, it is required to build a system able to generating maximum power beneath these constraints [1].
From the wind speed, wind turbine systemsproducts the electrical energy after converting wind speed to mechanical energy by the generator. Several wind turbines use the doubly fed induction generator (DFIG) using wound-rotor or cage type rotor [2]. The connection of the wind turbine to the generator with the gearbox causes the problems related with variable-speed wind systems. Nowadays, PMSG's are favored due to their, high-power density, lightweight, and high efficiency. Such machines are often directly connected to the turbine removing the need of a gearbox. This reduces the overall cost and reliability of the system [3]. The schematic block diagram of the overall system is presented in Figure 1.
The power output from wind turbines varies nonlinearly with enormous and sudden variations in wind speed, therefore the use of an MPPT controller is indispensable to optimize the generator speed and power output measurements in order to maximize the output power whatever wind speed. The control algorithm allows reaching and tracking the maximum power point MPP at all wind velocities. Over the years, several control methods have been proposed for extracting maximum power from wind to overcome various constraints such as Optimal Tip Speed Ratio Control [4,5] has developed nonlinear proportional complex integral (PCI), fuzzy controller [6,7], artificial neural networks (ANN) [8], robust control [9], DTC based  [10], direct adaptive fuzzy-PI controller and using ANN-PSO wind speed estimator [11], robust adaptive neural controller [12,13] has proposed Experimental enhancement of fuzzy fractional order PI+I controller of grid connected variable speed wind energy conversion system. This study presents a FFOPI controlled MPPT system suitable for the permanent magnet synchronous generator operating at variable speeds. The MPPT systemmethod uses FLC to creäte the reference speed that maximizes the extracted power from the turbine. In the same part the fractional order PI algorithm is used to attain the speed control of the generator for each wind speed extracting maximum power output of turbine. The remainder of this paper is ordered as follows: In Section 2, the system modeling is described. Section 3 presents in detail the proposed control strategy. Section 4 is devoted to present the simulations results. Finally, the paper is concluded in Section 5.

SYSTEM MODELING 2.1. Wind model
The wind speed is modeled by a sum of numerous harmonics as follows [14]:

Turbine's model
The turbine rotor reduces the air speed and at the same time transforms the absorbed kinetic energy of the air into mechanical power. The mechanical power of the wind turbine is given by [15]: (2) where, is the captured wind power (W), is the air density (kg/m3), R is the radius of rotor blade (m), is wind speed (m/s), and is the power coefficient. is defined as: where: is the turbine rotational speed. The value of power coefficientCpis depends on tip speed ratio (λ) and blade pitch angle (β) based on the turbine characteristics governed by [16]: where: 1 to 6 signify characteristic coefficients of wind turbine [16]: So, any variation in the wind speedor the rotor speed induces variation in the tip speed ratio leading to power coefficient change. In this way, the produced power is affected. Figure 2 displays a group of typical Cp-λ curves. The maximum value of the power coefficient is given for a null pitch angle and it is equal to: C pmax = 0.48 Matching to a specific optimal tip speed ratio identical to: Power coefficient curve

Model of PMSG
To simplify the response study of the generator it is useful to transform the equations from the stationary stator frame into the d-q axis using Park transformations [17]. The simple dynamic model of the PMSG in d, q frame can be denoted by the following equations [18]: (6) where , (V) are the direct and quadrature mechanisms of the generator voltages, Rs, Ldand Lq, one-to-one, are the resistance, the direct and the quadrature inductance of the PMSG winding, (wb) signifies the magnet flux, (rad/s) is the electrical rotational speed of PMSG , (A) are the direct and quadrature mechanisms of the generator currents, respectively. The mechanical dynamic equation of PMSG is governed by [19]: The electromagnetic torque of a p-pole machine is obtained as [19]: where (N.m) is the electromagnetic torque, is the number of pole pairs, is the damping coefficient, is the moment of inertia.
T T

PROPOSED MPPT CONTROL STRATEGY
The proposed scheme presents a fuzzy fractional proportional integral controlled maximum power point tracking system appropriate for the permanent magnet synchronous generator at variable speed wind turbine. Several schemes have been proposed to extract MPP from variable-speed wind turbines [20]. Figure 3 shows the proposed algorithm based on the cascade control algorithm FLC with fractional-order PI controller to permanently extract the optimal aerodynamic energy in order to produce the electromagnetic torque reference for each wind speed whereas, the control of the d, q-axis current of the generator, in the interior loop according to the (8) and by field-oriented control strategy (FOC) of the generator to ensure that the system workingsnearby the optimal point, which agrees theextraction of the maximum power by the turbine [21]. In this study it is supposed that pitch angle β have a tendency to zero, so that the power output , differs non-linearly with the turbine angular speed ( ) and variable wind speeds ( ). Hence, the FLC is used to guarantee a rapid and smooth tracking of the maximum power without the knowledge of the characteristic of the turbine and the wind speed measurement for generating a reference speed ( ) at which the wind turbine should operate, so that maximum power is shaped at the prevalent wind speed. Therefore, a FOPI method is proposed to achieve the speed control of PMSG for each wind speed in the objectif of maximize the extracted power at the turbine output.
The strategy structure of the MPPT method is given in Figure 4. The proposed FLC controller has two inputs ( , ) and a single output ( ). They are respectively given by: k: sampling instant  Fuzzification The framework introduces Mamdani inference mechanism [22] to build the fuzzy rule. Forty nine rules with seven fuzzy sets were used in this controller namely, Ng (Negative grand); Nm (Negative medium); Ns ( Negative small); Zr (Zero); Ps (Positive small); Pm ( Positive medium); Pg (Positive grand),  Fuzzy rules Later, the fuzzificationphase of the inputs, a fuzzy inference machine is defined by the whole of IF-THEN rules to linkage the inputs to the output. Based on the exact and accurate knowledge of the VSWT comportment, these heuristic rules are expressed in fuzzy field which are summarized in Table 1.   Fractional-order calculus (FOC) is one of the popular and emergent mathematics branches that deals with differentiation and integration of real or complex order [23][24][25]. Fractional-order mathematical phenomena are very useful to define and model real-time system more precisely than the conventional integer methods. The fractional-order differentiator can be represented by aoverall fundamental operator as a generalization of the differential and integral operators, which is defined as follows [25] is the Euler´s Gamma function, a and t are the limits of the operation, and is the integral fractional-order which can be a complex number. In this paper, is assumed as a real number satisfying 0  1. Also, a is taken as a null value and the following resolution is used: 0 tt DD    Based on the Riemann-Liouville,in the time domain the fractional order FOPI controller transfer function can be rewritten as follows [27,28]: In the fractional order FOPI controller, the weighted error is integrated instead of the error value. In this weighted integration, at time t, the function: In simulation and practices, the implementation of the fractional order term ( ) must be approximate by an integer transfer function, whereas a few methods have been established. Oustaloup's continuous approximation (OCA) is very used to approximate the fractional order ( ) to integer transfer function [29]. The parameters of the simulated system and the controllers used are respectively given by:

RESULTS AND ANALYSIS
The simulations results are made in the Simulink interface of Matlab. The parameters of the PMSG used in this paper are showed in Tables 2 and 3. Figure Table 4, it can be observed that the proposed controller FFOPI provides better performances to extract maximum power point for variable wind profile than FOPI and the PI controllers.

CONCLUSION
Variable speed wind turbine systems havebeen getting widest attention among the various renewable energy systems, the use of an MPPT algorithm is indispensable for enhancing energy capture performance of VSWT. In this work, a FFOPI controller is designed to track maximum power point from PMSG integrated in variable speed wind turbine. The scheme performances are compared with those obtained with fractional order proportional integral and conventional PI controllers. The simulation results prove that FFOPI controller provides better performances than FOPI and PI controllers in rapports of robustness, efficiency and response time. The simulation has been done using Matlab/Simulink® platform.