Fuzzy sliding mode power control for wind power generation systems connected to the grid

Received May 19, 2021 Revised Jan 31, 2022 Accepted Feb 7, 2022 In recent years we have witnessed a real increase in the production of wind turbines and wind farm installations around the world, in order to improve this own energy, several studies have focused on the interest of controlling the active and reactive power of the system. Wind power, and at the same time on the quality of the energy produced and its connection in order to ingest suitable electrical energy into the distribution network. This article studies a new control technology to meet the various constraints in the field. The objective for work is to develop and study the sliding mode control method applied to a wind power system based on doubly fed induction generation (DFIG), as well as an optimization using the fuzzy logic technique. Ensuring the stability of the system is one of the objectives of using the Lyapunov nonlinear technique in the sliding mode control strategy which will be applied to the two converters (machine side and network side). The proposed solution was to validate a simulation on MATLAB/Simulink, tracking test (true wind speed) and also the robustness of the system.

In recent years we have witnessed a real increase in the production of wind turbines and wind farm installations around the world, in order to improve this own energy, several studies have focused on the interest of controlling the active and reactive power of the system. Wind power, and at the same time on the quality of the energy produced and its connection in order to ingest suitable electrical energy into the distribution network. This article studies a new control technology to meet the various constraints in the field. The objective for work is to develop and study the sliding mode control method applied to a wind power system based on doubly fed induction generation (DFIG), as well as an optimization using the fuzzy logic technique. Ensuring the stability of the system is one of the objectives of using the Lyapunov nonlinear technique in the sliding mode control strategy which will be applied to the two converters (machine side and network side). The proposed solution was to validate a simulation on MATLAB/Simulink, tracking test (true wind speed) and also the robustness of the system.  [3]. In the immediate future, the world experiences a recourse to renewable energies, which present inexhaustible resources. Among which we find wind energy identified as one of the most promising for achieving greenhouse gas emission reduction targets. The exploitable renewable energies are numerous and varied. That said, the development of wind energy is booming, so wind systems are developing more quickly because we can now rely on reliable and proven techniques with better performance. Wind energy therefore remains the most used in energy production technique, hence the case of Morocco, which relies on wind energy production as the primary source of renewable energy with 4699.4 GWh in 2019 against 1581, 50 GWh for solar and it is considered the country's second energy source against 32,218.50 for thermal energy, i.e. a rate of 11.7% of the country's total energy production [3], [4]. The Figure 1 shows the graphic of energy production in Morocco.

Keywords
Currently, the majority of wind turbine installations in the world used DFIG-Generator. Because this type of machine has the ability to produce electric power at variable speed. The control of the studied system based on double-fed machines by classical methods (proportional, integral and derivative action) implies the knowledge of the various parameters, which can influence it and allow the system to achieve the set results. In addition, the strongly coupled variables, increasing the system, makes control more difficult. Using nonlinear methods is one of the solution to solve this problem like the sliding mode controller (SMC) control. The latter is considered one of the simplest approaches to control nonlinear systems and systems with imprecise models [5]− [10].

WIND ENERGY CONVERSION SYSTEMS (WECS) MODEL
The Figure 2 presents the wind energy structure. It contains the doubly fed induction generator, the converter, the filter and the grid. The control is showing in the input of the converter. "P R = P vent . C p (λ, β) The total kinetic power in the wind turbine is: For the production of wind turbines, it is necessary to take into account the defined range of the energy extraction coefficient which is generally between 0.35 and 0.5.
The equation of the aerodynamic torque (Tr) whose coefficient curves.
The following two equations used to model the adaptation of the two turbine speeds to that of the generator.
It is necessary to have a simulation tool capable of modeling the entire energy conversion chain and predicting its performance. Initially, a model of the wind generator is proposed under MATLAB/Simulink to evaluate its dynamics and its performance under different operating parameter changes. Figure 3 shows the model of bloc turbine in MATLAB/Simulink.

Pitch control and mechanical control
In-order-to better control the operation-of-the machine, a number of parameters must be defined beforehand on which the operation and behavior of the machine depends, such as:

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− The wind speed which allows defining the parametric changes of the machine, − The nominal power on the wind-turbine shaft, − The speed reference which corresponds to-the power − The starting speed is the minimum wind speed can start to operate and provide energy. − The safety speed is the wind speed which when it is exceeded the wind-turbine automatically stops working.
The turbine operating power diagramed is divided into four zones defined according to the wind speed Vn, Vd and Vm witch presented in Figure 4 the first zone corresponds to P=0 the turbine is not yet working. The second zone corresponds to the phase where the power supplied depends on the wind speed. The third is when the supplied power stabilizes at Pn for a constant speed of rotation and in the end the fourth zone which corresponds to the stopping of the energy transfer for safety reasons [14]− [19] Figure 5 shown the turbine has greater efficiency for low stall angle values. A single control loop may be sufficient to control the pitch for angle β to manage the orientation of the wind turbine blades. The rated power is controlled by a single servo loop and which is read with an open loop for controlling the orientation of the blades or the output of the first is the values of the pitch angle of the second. and therefore, we have two servo loops, one for nominal power control the second is for wedging angle control.

Power control technic
In order to limit the extracted power from the turbine so that it is equal to the nominal power of the generator, two principles of aerodynamic control can be used [20]− [24]: he first is the "pitch control" or not variable "which is based on the rotation of the blades by electric or hydraulic actuators which makes it possible to adjust the pitch angle β, which is called the blade orientation mechanism. it is therefore a principle which allows the mechanical adjustment of the turbine in order to keep it at its maximum efficiency.
The second principle is the "aerodynamic stall" considered more robust and the simples. The moment when the wind speed exceeds the nominal speed of rotation of the turbine, a suction thus created by the inclination of the blades which will not be in the same optimal position leads to a reduction in the power coefficient. Therefore, this inclination limits the increase in the speed of rotation. The interest of the first check can be observed from Figure 6.

Generator modeling
The generator we used for wind power conversion is the dual-feed asynchronous generator DFIG. [25]− [27]. The DFIG Model is schematized in Figure 7 is a in the park referential model, using the following equations: Figure 7. DFIG model

Stator and rotor voltage
The following equations define respectively. The stator and rotor voltage related to stator and rotor flux. We use in this definition park referential.

Stator and rotor currents
Using the park referential. We define the following equations respectively. The stator and rotor current related to stator and rotor flux

Stators and rotor flux
In the same referential dq we will define. The stator flus related to stator and rotor currents. The rotor flux related to stator and rotor currents and the electromagnetic torque relative to rotation speed φ ds = L s I ds + MI dr φ qs = L s I qs + MI qr (11) φ dr = L r I dr + MI ds

Stator and rotor powers
The (13) describe the active and reactive power of the stator in a two-phase reference system relative to current and voltage. The active and reactive power of the rotor in a two-phase reference system relative to current and voltage.

DFIG model
The following equations determine the electromechanical torque Figure 7.
T em = p(I ds . φ qs − I qs . φ ds ) The reference frame used is the d-q reference frame related to the rotating field of the stator, and by considering the hypothesis for the generators used in wind energy the resistance of the stator will be neglected, this said the equation of the torque will be:

SLIDING-MODE-CONTROL APPLIED TO THE DFIG
This method consists in first determining the adequate sliding surface, as well as the equivalent and non-linear value for each quantity to be regulated [27]− [29].
: Desired variable This command is based on the principle to keep the surface at zero, so we can have just one solution of the differential equation" ( ) = 0".

Conditions of convergence
The convergence condition is defined by the lyapunov equation [29]."

Determination of the control law
The command ( ) is a variable structure command and the control algorithm is defined by the relation [29]. The saturation function can be expressed by [27], [28]:

The sliding mode application
This part is devoted to the application of the control by sliding mode in the asynchronous generator with double feed. Following the new considerations, the previous become as such:

ACTIVE POWER CONTROL SURFACE
Considering the sliding surface by J. Slotine given by: We consider = 1, We have the active power control surface the: S(P s ) = e(P s ) = P sref − P s S(P s ) = P sreḟ − P ṡ We replace ̇ by its expression as well as ̇, we get: S(P s ) = P sreḟ + V s .
The control is given by: With: : Positive gain

REACTIVE POWER CONTROL SURFACE
With the same method as the active power, we find: We replace ̇b y its expression as well as ̇, we get: and discontinuous control is given by: with: : Positive gain

SLIDING FUZZY MOD CONTROL
The sliding mode control maintains robustness and improves system performance. However, the command switching term produces a chattering phenomenon which is its main flaw. overcome this problem, we propose the model that combines between fuzzy logic control "FLC" and sliding mode control "SMC" [30]. The sliding mode control law is defined by the control strategy, which depends on the sign of the error if it is negative, and then the system output is driven in the positive direction.
For this the term K d . sat(S(U n ) can be replaced by a fuzzy controller. This controller has an input S(x) and an output U n and its rule base is used to establish a connection between S(x) and U n . This is interpreted by the rules of the form (If… Then) [31], [32]. We design for this purpose a command by fuzzy sliding mode to control the active and reactive powers as presented in Figure 8 The basic input and output linguistic variables of the fuzzy control rule are presented in Figure 9. In this section, the FLC fuzzy command is introduced to replace the K d . sat(S(U n ) function, good steady-state dynamics can be obtained applying fuzzy logic to the DFIG speed command by combining it with the sliding mode command. The verification of the advantages of this new fuzzy sliding mode command will be carried out by simulation. The speed and rotor flux regulators are replaced by a sliding-fuzzy mode regulator.

SIMULATION RESULTS
In purpose to present the evaluation of the performance of the new hybrid fuzzy sliding mode control SFMC, we will expose the simulations carried out on an asynchronous machine with double power supply, Figure 10 represents the block diagram of the simulation of the principle of the fuzzy sliding mode control applied to DFIG, replacing the sign (S w ) function with a crazy controller. Figure 10. Sliding mode control applied to DFIG

Performance test
We will study and analyze the response of the DFIG for a wind profile that we choose to be random. In order to improve the quality of the electrical energy injected into the network, we are going to set the reactized power to zero. (Qs_ref = 0 Var). The wind profile used in the simulations presented is a real wind profile. The results of the responses of the fuzzy logic mode sliding control of the DFIG are represented in Figure 11 (see Appendix) shows the chosen winds are that of the Tanger region located in the north of Morocco. The Figure 12 shows THD for the rotor current "6.29%" and "0.16%" for the stator current (according to standard IEEE519-2014).

Robustness test
We are going to make some modifications to the internal parameters of the DFIG to verify the robustness and stability of the fuzzy sliding mode control on active and reactive power regulation. On this, the tests carried out are carried out on the basis of an increase and decrease of the parameters of the machine such as the stator, the resistances and the inductances of the rotor. Thus, the dynamic behavior of the system is represented in Figure 13. Figure 13. Robustness test during resistance variation However, the changes applied to the resistances of the stator and the rotor cause a slight increase in the response time, which is detected in Figure 13, we therefore notice that the simulation results show a great robustness of the fuzzy-sliding mode command with respect to the parametric variations of the DFIG. This is justified by the good follow-up of the power setpoints, with almost the same response time at start-up. It always maintains the decoupling between active and reactive power. This performance is showing in Table 1.

CONCLUSION
In this article, we have presented the control of a wind energy recovery system equipped with a doubly fed induction generator. Firstly, a generator model was proposed, and then a fuzzy sliding mode control strategy of the asynchronous generator allowing independent power control was proposed. Fuzzy sliding mode active and reactive power regulators have been proposed and tested. The simulation results enabled us to assess the performance and robustness of the fuzzy sliding mode control. Thanks to the response characteristics, good performance is observed even in the presence of set point variations. The pursuit of power is without overshoot. Decoupling, stability and convergence towards equilibrium are ensured. In addition, this setting has the advantage of being easily implemented in a computer control. Figure 11. Performance test of the SFMC applied to the DFIG  ISSN: 2088-8694