Performance enhancements of DFIG wind turbine using fuzzy-feedback linearization controller augmented by high-gain observer

Received Apr 17, 2019 Revised Jul 22, 2019 Accepted Aug 12, 2019 This paper proposes a feedback linearization control of doubly fed induction generator based wind energy systems for improving decoupled control of the active and reactive powers stator. In order to enhance dynamic performance of the controller studied, the adopted control is reinforced by a fuzzy logic controller. This approach is designed without any model of rotor flux estimation. The difficulty of measuring of rotor flux is overcome by using high gain observer. The stability of the nonlinear observer is proved by the Lyapunov theory. Numerical simulations using MATLAB-SIMULINK shown clearly the robustness of the proposed control, particularly to the disturbance rejection and parametric variations compared with the conventional method.


INTRODUCTION
The wind energy is a pollution-free and effective source. Therefore, a wind power generation system becomes one of the potential sources of alternative energy for the future [1]. Energy consumption over the last century has increased significantly due to the great industrialization. Recently, particular interest has been given to generating electricity from renewable energy sources. Of all renewable sources, wind energy holds the largest market share and is expected to maintain rapid growth in the coming years [2]. Wind energy systems have received considerable attention over the past decade as one of the most promising renewable energy sources due to negative environmental influences and the high cost of conventional energy sources. In this context, several countries have turned to explore the wind energy sector, leading researchers to conduct research to improve the efficiency and power of electromechanical conversion and quality of providing energy [3].To meet energy needs, it is imperative to find adjusted and flexible solutions by reducing energy consumption or increasing energy production by adding power plants or improving the efficiency of existing installations. In addition, the dynamic improvement of the performance of renewable energy systems, whose non-linear characteristics are particularly important, especially with the rapid growth of their use. Therefore, the control of the Wind Power Conversion System (WECS) based on doubly feed induction generator (DFIG) with intermittent input wind speed is particular interest in the energy and control communities. DFIGs are potential candidates for high power wind systems because they can generate reactive current and produce constant frequency power for variable speed operation. However, the main disadvantage of the DFIG is its brushes and slip rings structure, which involves permanent maintenance and reduces the life time of the machine [4]. This type of generators has been widely used for wind systems [5]. The control and operation of these systems has been the subject of many research projects in recent years [6]. In this perspective, various studies have been proposed in [7][8][9] to control wind turbine systems based DFIG from the classical configurations by application of Field oriented control (FOC) strategy. However, the WT-DFIG is highly nonlinear system, with strong couplings between the different variables of the systems. In this context, many nonlinear control methods have been developed. Penghan Li et al [10] proposes a non linear controller based on state feedback linearization strategy to reduce sub-synchronous control interaction inseries-compensated doubly fed induction generator (DFIG)-based wind power plants.
In [11] the authors have used a robust nonlinear feedback linearization controller based sliding mode control to relieve sub-synchronous control interaction in doubly-fed induction generator based wind farms connected to series-compensated transmission lines. The two aforementioned works show good performances. However, the authors did not use a nonlinear model and DFIG Wind Turbine control scheme is based on vector control. In addition, the states of the DFIG are supposed to be measured.
Djillali et al [12] have used Neural Input-Output Feedback Linearization Control. The neural controller is based on a Recurrent High Order Neural Network, trained with an Extended Kalman Filter. This last method uses a simple PI controller to define the control law defined by a relationship linking the new internal inputs to the physical inputs. The same strategy control has been applied in [13] based on the linear quadratic regulator (LQR). Due to the limitations presented by the two linear controllers the PI and the LQR which have a low robustness to parameter variations as well as to unbalanced grid voltage which have direct effects on the dynamic performance of the system, and poses serious problems, such as oscillations of the stator power and the generator torque, which are detrimental to the mechanical system and the electrical network [14].
In this paper the Feedback linearization technique is combined with Fuzzy logic to form Fuzzy-Feedback Linearization Controller applied to a non-linear model of DFIG to improve the performance of the system such as the response time , robustness against parameter variations and the sensitivity to perturbations (unbalanced grid voltage) .This new method is augmented by High Gain Observer (HGO) mainly used to estimate generator rotor flux, based on the measurement of rotor currents ,stator voltages and the mechanical speed. The effectiveness of the proposed controller is compared to the conventional Feedback linearization control by simulation results in Matlab Simulink.

MODELING OF STUDIED SYSTEM
As shown in Figure 1 the system is composed of two parts; the first is the conversion of the kinetic energy of the wind into mechanical energy via a turbine and the second is the conversion of the mechanical energy at the level of the turbine shaft into electrical energy via a double-feed generator. The stator is connected directly to the grid and its rotor also via a static converter which allows delivering the necessary control voltages of the stator powers.

Turbine model
The aerodynamic power appearing at the rotor of the turbine is then written [15].
Where: ρ is the air density and S the swept surface area of the turbine (πR V is the wind speed (m/s), C λ, β is the power coefficient of the turbine, λ is the tip speed ratio and β is the pitch angle. The tip speed ratio is: where: R is the radius of the turbine (m) and ω is the speed turbine (rad/s). Figure 2 shows the curve of the power coefficient versus λ for a constant value of the pitch angle β.

Dynamique model of DFIG
The mathematical models of three DFIG phases in the Park frame are written as follows [16]: Where R , R are the rotor and stator resistances, respectively; L , L , M are the rotor, stator and mutual inductances, respectively; i , i are the stator-rotor current components; v , v are the components of the stator-rotor voltage; φ , φ are the stator-rotor flux components; ω , ω are the rotating and stator pulsations, respectively.
The model of DFIG according to the rotor components is represented by the following equations [15].
where P is the number of pole pairs; J is the inertia of the shaft , C is the torque on the generator .All frictions on this shaft are included in C . We put The system (6) is then written in the form:

FEEDBACK LINEARIZATION CONTROL
To develop nonlinear control of the active and reactive powers of stator, the feedback linearization strategy is proposed. This technique consists to transform nonlinear systems into linear ones, so that linear control techniques can be applied. This technique is possible through change of variables and by choosing a suitable control input [17].According to the model of the DFIG developed above, and recalling that the reference is chosen so that its component (d) coincides with the stator voltage vector, this system has as input variables the voltage applied to the rotor v v and as output variables the active and reactive power at the stator P , Q defined by: The stator powers' control law is computed according to the rotor current measurement and estimated rotor flux. The latter comes from the proposed high gain observer. Substituting i and i in (10) by their counterparts extracted from the two last equations of (4), one has: Differentiating (12) until an input appears Write the last equation as follows It is desired to regulate the output quantities P and Q to their respective reference value P and Q For this purpose defining the adjustment errors Defining the input of the DFIG system Rewriting (14) in the matrix form Rewriting the new inputs V and V in the form (18) From (19) we can write From (17) and (18) the control law is given as where The reference active power Ps is generated by MPPT and the reactive power Qs is defined by the grid to support the network voltage .To follow the trajectory of * and Q * , we use a PI controller imposed to the linearized system [17]. The new input v is given by

HIGH GAIN OBSERVER FOR FLUX ESTIMATION
We intend to construct such an observer, based on the measurement of the rotor currents, speed and voltages [15] the principle is shown in Figure 3. The estimated flux components φ , φ are used in the computation of the FBL law.We propose to implement a rotor flux observer in order to study its properties.
From the model (7) and assuming the constant velocity (Ω = 0), with Ω ω we can write: where A Ω , B and v are given by Thus, at constant Ω, the model is linear, which is a particular case of the form of injection of the output and of the output derivative.
In this part, we are interested in the work presented in [18,19] which deal with the synthesis of observers with high gain for locally observable systems.
Then it is possible to make out the following change of variables: For these changes, model (7) takes the following form: We put That transforms the nonlinear system (28) into a local system of pyramidal coordinates With the output vector C , 0 Then the following system z z ψ z , z S θ C Cz y Is exponential observer of the system with S θ is the matrix defined by With θ 0 Is the unique solution of the following Lyapunov algebraic equation:

Theorem
The function ψ is globally Lipchitzian with respect to z uniformly with respect to v and v ‖ψ z , v , v ψ z, v , v ‖ ‖z z‖ (35)

Proof of stability anaylsis and observer convergence
Consider the error e z z Its dynamics is given by Using inequality C C 0 and theorem (1) we can increase V e as following: V e e θS θ e 2 e S θ e θ 2 V e (41) This guarantees the exponential stability of the observer for θ 2 this concludes the proof.

Observer in the initial coordinates
The observation x of the state x for the model (7) is obtained by: Is a method of synthesizing the observer expressed in x Or in the panoramic form:

FUZZY-FEEDBACK LINEARIZATION CONTROL
Fuzzy logic control has been widely used in recent years due to its simplicity of implementation and its ability to control nonlinear systems, which gives better performance under parameter variations and voltage disturbances [20].
Based on the study of fuzzy logic control described in [21], [6] we will proceed to its application to DFIG based on the equation (19) or we consider our system as a simple integrator which facilitates the synthesis of this control where we will have two regulators on each of the loops, that of the active power and that of the reactive power. Figure 5 shows the principle of the proposed method. The two most significant quantities to analyze the behavior of the system namely the power error e , and its variation de , are chosen as two inputs of the regulator by Fuzzy logic controller FLC.   For the defuzzification of the output variables of the system, we use the method of the center of gravity (COG) [22].
The proposed control is represented in Figure 7.

SIMULATIONS AND RESULTS
In what follows we will study the performances (Reference tracking, disturbance sensitivity and robustness) for different controllers mentioned above conventional feedback linearization control (CFBL) and proposed Fuzzy-Feedback Linearization control (PFBL) using the rotor flux observer.

Reference tracking
This test consists in making a change in the active and reactive power setp values while maintaining the drive speed of the generator constant. Figure 8 illustrates the behavior of active and reactive powers stator. By examining this figure, it can be seen a good reference tracking with a less ripples for the proposed method compared with the conventional method. The decoupling between the two powers is ideally noted for the proposed method contrary to the conventional method we notice the appearance of a static error at times of step change (see Figure 9). In Figure 10, the observer's performance is illustrated when the estimated rotor fluxes and real fluxes are substantially identical for the dq axis.

Disturbance sensitivity
This test use to verify to what extent the measured powers stay at their reference when the grid voltage drops by 20% between 0.8s and 1.3s. The effect of this fault on the active and reactive powers of the machine is illustrated in Figure 12.
The power references are correctly tracked, except for the presence of oscillations which are greatly increased during the fault, the power measurements show a significant deviation from the value of the reference and a reset time greater than 400 ms in the case of a conventional controller compared with the proposed controller which more effectively rejects the voltage drop effects (see Figure 13). The performances of the observer are verified by the simulation results presented in Figure 14. It can be clearly seen that this  Figure 15).   Figure 16 shows the evolution of the active and reactive powers during a parametric variation of the generator when the resistance values are increased by 200% and the inductance values decreased by 60%. These results show that the excessive parametric variation caused a clearly degradation of the active and reactive powers curves with the appearance of a static error in the case of the conventional controller. The response of the system with the proposed controller remains insensitive to these variations.

CONCLUSION
This work presents a feedback linearization control improvement for a DFIG-based wind system. In this context, we applied the fuzzy logic controller to the feedback linearization strategy. This is intended to improve the performance of the system particularly against parametric uncertainties and disturbance sensitivity that have an effect on conventional feedback linearization control used PI. From the comparative results between the two approaches presented, it can be concluded that intelligent controller have significant improvements to dynamic performances over conventional controllers. In addition, a part was reserved for the synthesis of a high-gain observer to reconstruct non-measurable rotor flux components for technical and economic constraints. This observer is tested by numerical simulation in combination with the adopted control that meets the assigned objectives.