PSO-Backstepping controller of a grid connected DFIG based wind turbine

Received Feb 23, 2019 Revised Sep 5, 2019 Accepted Sep 27, 2019 The paper demonstrates the feasibility of an optimal backstepping controller for doubly fed induction generator based wind turbine (DFIG). The main purpose is the extract of maximum energy and the control of active and reactive power exchanged between the generator and electrical grid in presence of uncertainty. The maximum energy is obtained by applying an algorithm based on artificial bee colony approach. Particle swarm optimization is used to select optimal value of backstepping’s parameters. The simulation is carried out on 2.4 MW DFIG based wind turbine system. The optimized performance of the proposed control technique under uncertainty parameters is established by simulation results.


INTRODUCTION
The use of energy plays a vital role in making industrial and manufacturing process much more efficient. However, due to this large use, the production of unwanted materials that pollute air and contaminate soil and water was spawned an increase. In this way, the maximum rate of petroleum extraction has been reached and that subsequent methods of extraction cannot increase the rate further. One optimal solution to this problem is to use renewable energy sources. Their interest is that they do not emit greenhouse gases and produce no toxic and radioactive waste. Wind energy is one of the purest and eficient energy in the world for the production of electricity. The kinetic energy of wind is harnessed by wind turbines and converted into mechanical energy and finally into electrical energy.
Quite recently, a large variety of publications have been undertaken for doubly fed induction generator modeling and control, in which vector control combined with proportional-integral (PI) loops is widely used in industry, due to its simple architecture, big advantages of decoupling active and reactive power, in addition high efficiency [1]. The main purpose of DFIG control system is to efficiently extract the wind power whatever the weather conditions, this is usually named maximum power point tracking MPPT [2][3]. A substantial review of this control is given on [4]. Meanwhile, an approach to attenuate the impact of failures in DFIG generator based wind is often required, so that DFIG can withstand some typical disturbances wind system. However, the major deficient of vector control is that it cannot keep a high level performance when parameter's system vary as its PI parameters are fixed, while system nonlineaty on DFIG is strong resulted from the fact that is a typical time-varying dynamic system with parametric uncertainties. Many efficient parameters tunning methods have been proposed to enhance the PI controller,  [5][6][7].
In fact, the second order sliding has been used to regulate the wind turbine system in accordance with references provided by Maximum Power Point Tracking algorithm in [8]; in reference [9] a controller based on direct-current vector has been used in DFIG to extract the maximum energy and control the reactive power. The adaptive feedback linearization controller has been developed in [10]. A nonlinear predictive controller has been proposed to extract power and transient load reduction by using predictions of the output power to optimize the control of sequence in [11].
In the literature, several theories have been proposed to explain the effectiveness of backstepping control; in [12], a backstepping controller is developed for standalone DFIG to control the stator output voltage and fulfilling the demand energy variations and impact of wind velocity. In [13] the mechanical and electrical parts of the system are controller by rotor currents. In [14] the author's attention are not focused in regulating the mechanical part, they just apply the control strategies to the generator side converter by combining the feedback form of backstepping with two takagi-suggen fuzzy system. In [15], authors compares PI controller and backstepping approach for controlling independently the extracted active and reactive power from the stator of DFIG to electrical grid. In [16], electrical and mechanical parts are controlling by using stator currents as references.
For our knowledge, any paper has taken into consideration the impact of rapid variation of wind and DFIG's parameter uncertainty on the performance of controller.The objective of this paper is the control of active and reactive power extracted using backstepping control taking into consideration the DFIG's parameters variations which increases control efforts. Generally, the selection of backstepping's parameters is arbitrarily, in this work, we determine the best parameters of the backstepping controller by using particle swarm optimization (PSO). In addition, artificial bee colony (ABC) algorithm proposed in [17] is used to maximize the extracted power by adjusting the rotor speed, according to wind speed, without knowledge of system parameters.

WIND TURBINE SYSTEM MODELING
In this work, the considered system is a large variable speed wind turbine. Its architecture is shown in Figure 1. The most important parts of the system are composed of two components. The mechanical part is composed of a rotor entrained by kinetic energy of wind and a gearbox, which makes the high-speed shaft to the right. The electrical component contain a DFIG and converters.

Mechanical model
The mechanical power received by wind turbine system WTS is defined as: The relation between , λ and β is defined by [18] : With: The formula of the tip ratio is provided by: Where Ω is the rotor speed. Furthermore, the mechanical torque on the rotor is calculated by: The mechanical angular speed and torque on the axis of generator DFIG is given by: M is the multiplication ratio.
In order to calculate the mechanical angular Ω , we apply the fundamental equation of dynamic: Where J is the total rotational inertia and is electromagnetic torque. The damping coefficient f is overlooked because it is lowest than rotational inertia [19]. Therefore, the mathematic equation which model our system is:

Electrical model
The electrical model of the DFIG in dq reference are given by [3]: With: With: = -and = - , rotor and stator cyclic inductances , : stator and rotor inductances. , : Mutual inductances; M= Max( , ). The electromagnetic torque and power equations at the stator are expressed by [20]:

POWER CAPTURE OPTIMIZATION
The evolution of the power extracted from a wind turbine according to the speed of the wind is presented in the Figure 2.  Figure 2, the system is designed to operate with a specific interval of wind speed. The limit of the range are known as the lower speed and top speed . In this interval, the controller must optimize the power extracted. This extracted power is usually dependent on the value of , which must be set at its optimum value . Therefore, β and λ must be optimal.
In order to fix an optimal tip speed ratio, the rotational speed ω of the rotor must follow the optimal value Most of the previous studies have not consider wind speed turbulence which increases control efforts. In this paper, a compromise between power capture efficiently and load reduction is obtained by a suitable selection of the controller bandwith.

POWER CONTROL APPROACH
The principal objective of the proposed control is capturing the maximum power of the incident energy of the system by adjusting the rotational speed, and control the active and reactive power of the system with large inertia exchanged between (DFIG) and the grid in presence of parameter's uncertainty such as resistance, inductance and tip speed ratio variations.

Maximum power point tracking (MPPT)
The MPPT algorithm is employed on region between Vcut and Vcout to capture maximum power point (MPP) for all wind speeds. In the literature, several MPPT algorithms have been discussed so far [21]. These methods are effective for wind turbine with low inertia. But, for high inertia, it takes more time and don't offer effective results. According to (1), whatever the wind speed, the maximum power extracted is obtained when power coefficient is optimum Figure 3. In this paper, a novel solution to MPPT based on Artificial bee colony algorithm [22] under variable wind speeds. Only one other study [23], to our knowledge, has come up with ABC based MPPT but without taking into account wind speed turbulence. The ABC algorithm includes three main groups: employed, onlooker and scouts. Each group has a well-defined role [17]. Employed bee exploits the food sources and carry the food source back to the hive. They share these foods with the onlooker bees by dancing in the designated dance area inside the hive. The onlooker bees select the optimal food. All food sources exploited fully, will be abandoned by employee bees and become scout. The process of the ABC algorithm is established in [17]. In this paper, with Artificial Bee colony (ABC), we determine the reference value of rotor speed Ω that should be applied to extract the maximum power. To concretize the control of Artificial Bee Colony based MPPT, each bee is defined as the rotational speed and the output power of system as the nectar amount. The initial rotor speed will become: New solution: new The fitness of each candidate is assessed by its generated output active power: The detail of the ABC algorithm used in this paper to determine the optimal speed is below:  Insert the maximum cycle MCN and number of initial candidate SN.  Generate randomly the rotor speed (employed bees) (18)  Calculate the power of each rotor speed (1).  Repeat:  Modify the rotor speed according to (19).  Evaluate the power of the new solution (1)..  Apply the greedy selection for each rotor speed.  Evaluate the probability according to (20).  fix the onlooker bees basing on the probability and edit each candidate (18)  Apply the greedy selection for each onlooker bees.  Fix the scouts bees and replace it by (18).  Memorize the optimal solution  Increment the cycle until Maximum cycle MCN.

Electrical part
According to (8), the nonlinearity of the generator's model is due to the coupling between the rotor speed and the currents. We annul the direct axis current in order to align flux ɸ in d-axis [24]. We obtain: Therefore from (10), we obtain: In addition, we notice that stator is connected to a stable grid,therfore stator resistive is neglected and the stator equation are reduced to: The stator powers can be expressed a: The double fed induction generator is controlled by rotor voltage. Therefore we should set the relation between currents and voltages of rotor circuit: The faults in DFIG are dominated by stator and rotor winding insulation faults, short circuits in stator circuit, variable resistance faults, cracked rotor end rings …. Equations. (7) and (27)  Where , , , , and are the rotor resistance and inductance variation, the stator resistance and inductance variation, and discrepancy in the calculation of and , respectively. By using partial derivative, we obtain: Ω̇= 0.5πρ 5 3 3

Application of backstepping controller in double fed induction generator
The studied system (31) is nonlinear; the linearization around operating point cannot be employed to design the controller. Therfore, we must apply one of the existing nonlinear control design. One of these methods, we use the nonlinear backstepping controller. The nonlinear Backstepping approach is a method that can efficiently linearize a complex nonlinear system in the presence of parameter's uncertainties. The essence of this method consists the decomposing of the system into many subsystems, design the Lyapunov function and virtual function for each subsystem. Therefore, it uses an error variable that can be stabilized by choosing the optimized control based on the study of lyapunov stability. Taking into account that the variation of parameters Δ , Δ , Δ , Δ , Δ and Δ are finite. Therefore, the function Δ1, Δ2 and Δ3 are bounded: | 1 |≤ 1 ; | 2 |≤ 2 ; | 3 |≤ 3

Step1:
In order to force the generator angular speed at the desired reference Ω and stabilize the error dynamic, we define the positive lyapunov function: The error tracking is defined as: The derivative of this function is: 3 In order to guarantee Ω tracks Ω , the derivative must be always negative. Therefore, must be chosen as: = 0.5πρ 5 3 3 With 1 ≥ 1 1 is the feedback gain. This choice makes Ω negative. After calculation of electromagnetic torque, the quadrature rotor current reference are: To maintain a unit power factor, the reactive power should be fixed at zero: =0 From (19), we obtain: Step2: The calculation of rotor voltage is primary to force the currents follow and . The lyapunov function is The derivative of lyapunov function is: By taking the following control and : With 2 and 3 are feedback gain. We obtain Which implies that our system is asymptotically stable. The choice of 1 , 2 and 3 is heuristic, for these we propose the PSO method to determine these parameters.

RESULTS AND SIMULATION
The simulation is realized in MATLAB/Simulink with the parameters of a 2.4MW machine. In order to verify asymptotic stability of our controller and show its performance, we implemented the system that includes wind turbine, (DFIG) and converter. The simulation has been realized for a wind speed from 6 m/s to 12 m/s as shown in Figure 4. Table 1 shows the parameters of the DFIG based wind turbine. In this paper, PSO is used to select efficient parameters of controller in order to converge rapidly to the optimal functioning. PSO algorithm introduced by Kennedy and Eberhart in 1995 [24], is inspired by social behavior of bird flocking or fish schooling, characterized as a simple structure. PSO algorithms use particles which represent potential solutions of the problem. It is first initialized with a group of random particles. In each iteration, every solution is modified at a certain velocity by following two best solutions (fitness). The personal best which is the best value achieved by each solution and the global best is the best value of all particles.
The position and the velocity of each particle of the population are defined as the following two equations: Where is the velocity of the particle, is the solution. 1 and 2 are random numbers. 1 and 2 are usually between 1.5 and 2.5 and finally ω is the inertia factor. The PSO algorithm used in this paper consists of the following steps: 1. Population of particles is generated with random position and velocities (parameters 1 , 2 , 3 of backstepping controller) (population size 50). In order to converge rapidly to the best solution, we minimize a certain criterion such as the mean square error can be calculated by the following equation: N is the total number of samples, T: the sampling time  The determination of speed reference Ω , which tracks the speed of the wind is given by Artificial Bee colony algorithm and then used by backstepping controller to regulate the speed of DFIG. The schematic of our control strategy is given in Figure 5. To verify the robustness of this proposed controller, PSO-Backstepping is compared with arbitrary backstepping controller which is implemented on recent works [26][27][28][29]. Figure 4 shows the simulation results without parameters variations and the zoom of these resultants, respectively. Based on the results, it can be seen that the rotor speed Ω, active power P and reactive power Q converge to their references with a precision rate.in addition, the power coefficient is optimal (Cp = 0,44), which indicates that the power extracted from the system is maximal. However, the backstepping controller with optimal parameters ( 1 , 2 and 3 ) based on PSO algorithm permits to converge more quickly to the optimal trajectory than the backstepping with parameters selected arbitrary. In order to evaluate the robustness of our controller with presence of uncertainty, we have considered Δ =Δ = Δ =5%, Δ =90%, Δ =6% and Δ =5%. It can be seen in Figure 6 that the robustness of our proposed controller does not affected by the variation of DFIG's parameters and the speed Ω, active power P and reactive power Q converge to their optimal values. In addition, the particle swarm optimization selects the best value of parameters for tracking rapidly the best trajectory.

CONCLUSION
From the outcome of our investigation, it is possible to conclude that the backstepping controller with particle swarm optimization can solve the challenge of controlling the power extracted in presence of DFIG's parameters uncertainties, which is due to technical problem in the generator. The ABC algorithm is applied to select the reference of rotational speed of wind turbine whatever the wind in order to extract the maximum power in real time. The robustness of the controller is demonstrated by simulation results.